Questions on (ordinary) differential equations. For questions specifically concerning partial differential equations, use the (pde) tag.

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182 views

Euler method on differential equation problem

I have this problem to solve. I want to compute the inclination of a plane $\theta(t)$ at every frame of a simulation given the following rule for its angular speed of rotation $\omega(t)$ $$ ...
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100 views

ODE can someone can help?

The factor $g(N) =\displaystyle r \left(1-\frac{N}{K}\right)$ in the logistic equation $\displaystyle \frac{dN}{dt} = \displaystyle r \left(1-\frac{N}{K}\right)N$ is a per capita growth rate. Smith ...
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76 views

Information about the reaction-diffusion equation

We´re modeling the distribution of a population on a 2-dimensional plane with the reaction-diffusion equation: $$\frac{\partial P}{\partial t} = \nabla (D(x,y)\nabla P) + rP(1-\frac{P}{k(x,y)})$$ ...
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251 views

Vector Field/Differential Equation Correspondence

I have seen some examples (though I am currently looking for a good rigorous explanation and a source would be much appreciated) of taking a second order linear ODE and turning it into a linear system ...
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176 views

Maximal Lyapunov Exponent

I am trying to figure out the equation below so that I can re-create it and use it for probability of dynamic systems in MATLAB. I am trying to figure out what the symbol stands for and how to use ...
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176 views

New system of two second order differential equations

I know one more thing from physical system. If we can assume the solutions in form $$x=Ae^{jp_1t}, \quad y=Be^{jp_2t}, \quad j=-1^{1/2}$$ I know that $$p_1=2p_2$$ If someone can help me. It is need ...
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44 views

Need practical help with a calculation

I'm sorry for a really basic question. I lack proper background in mathematics, but I have to calculate a list of values. I'm given a vector (list) of observations, and $\hat{Y}$, which is a list of ...
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296 views

A differential equation (nonlinear First-Order)

how to solve this equation: $(Px-y)(Py+x)=h^2P$ that $P=\frac{dy}{dx}$ and $h$ is a constant.
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462 views

Reduce a second-order ODE to first-order ODE plus a quadrature

Dear all, I'm trying to find the general second-order ODE admitting $$x* = \alpha x$$ $$y* = \alpha^{k} y$$ and reduce it to first-order plus a quadrature. The general solution I found by using ...
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1answer
162 views

How are the initial conditions transformed with a change of variable?

I have an ODE of the form $y''(x)=F(x,y')$ which has the initial conditions, $y(\mu)=\mu$ and $y'(\mu)=1$. Now I have seen that an equation which is equidimensional in x, can be made ...
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1answer
246 views

Determine the complete real solution to a homogeneous differential equation

Hello i am having some problems working out how to attack this assignment, and after spending hours on it, have i resolved to ask you guys here for help. I have been given the following differential ...
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1answer
62 views

How do I adjust model parameters to get stable oscillations with Arditi-Ginzburg equations?

I am using the predator-prey equations from the Arditi-Ginzburg to model the interactions of 14 species in a video game. The equations for two species are: $$ dx=x(A-Bx)-Cxy/(x+y)\\ dy=-Gy+Mxy/(x+y) ...
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2answers
137 views

How to solve$(2xy^2-3y^3)dx+(7-3xy^2)dy=0$.

How can we solve the following differential equation? $$(2xy^2-3y^3)dx+(7-3xy^2)dy=0.$$ I solved it by using change of variable $y=z^\alpha$ but I'm looking for other ways to solve it.
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1answer
69 views

Need help with boundary conditions of a differential equation.

QUESTION: A particle $A$ is moving along the $X$ axis at a constant horizontal velocity $u\hat{i}$. Another particle $B$ is moving such that its velocity vector always points towards the particle ...
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2answers
567 views

How do I show the Wronskian of $(J_{a}(x),Y_{a}(x)) = \dfrac {2} {\pi x}$

Based of using my undergrad class notes. I know that the wronskian of $(J_{a}(x),Y_{a}(x))$ is $ W(J_{a}(x),Y_{a}(x)) = \left| \begin{matrix} J_{a}(x) & Y_{a}(x) \\ J_{a}'(x) & ...
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1answer
244 views

Convert $\frac{d^2y}{dx^2}+x^2y=0$ to Bessel equivalent and show that its solution is $\sqrt x\left(AJ_\frac{1}{4}+BJ_{-\frac{1}{4}}\right)$

I have been following the thread " Convert Airy's Equation $y''-xy=0$ to Bessel equation $$t^2u''+tu'+(t^2-c^2)u$$ " but I can't join the dots to a solve similar equation $y''+x^2y=0$ so as to obtain ...
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3answers
106 views

A secondary nonlinear ODE

How to solve this particular ODE: $$\frac{d^2y}{dx^2}=\frac{a^2}{y^2}-\frac{b^2}{y^3}$$
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2answers
1k views

Solve $y' = x + y$

I am suppose to use the substitution of $u = x + y$ $y' = x + y$ $u(x) = x + y(x)$ I actually forget the trick to this and it doesn't really make much sense to me. I know that I need to get ...
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2answers
99 views

Help a beginner solve a differentials eqn

I need to determine whether the function defined implicitly by: $$x^2 + y^2 = 9$$ is a solution of the differential equation: $$\frac{dy}{dx}= \frac{x}{y}.$$ Please explain each step in process. I ...
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3answers
114 views

$y_1, y_2, y_3$ are particular solutions of $y'+a(x)y=b(x)$, so the function $\frac{y_2-y_3}{y_3-y_1}$ is constant.

I'd really love your help with the following exercise. I need to show that if $y_1, y_2, y_3$ are particular solutions of the linear equation: $y'+a(x)y=b(x)$, so the function ...
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3answers
3k views

solving second-order nonlinear ordinary differential equation

I am trying to solve the following: $$y''(x)=\frac{4}{3} y(x)^3 y'(x)$$ given that $y(0)=1$ and $y'(0)=1/3$. This is a link to Wolfram Alpha. My idea was that because when $y=1$, ...
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2answers
40 views

Differential Equation $ln(y') = x - y - e^y$

Find the solution to this initial value problem on the largest interval. $$ln(y') = x - y - e^y, \,\,\,\,\,\,\,\,\,\,\,\,y(1)=0.$$ So this differential equation is not linear and not homogenous. I ...
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2answers
33 views

Constant differential equation

What is the procedure for solving a simple differential equation: $y'(t)=C$, where C is a constant? What is y(t)? ${}{}{}{}{}$
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3answers
93 views

solving second order linear ODE

I do not know how to solve this differential equation: $$ \frac{a}{x}y'(x) + \frac{1}{2}y''(x) = 0 $$ where $a$ is a constant. Also how can I solve this equation if the right hand side ...
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3answers
157 views

Solving $y' = y-x-1+\frac{1}{x-y+2}, y(0)=0$

I have to solve the differential equation $$y'(x) = y(x)-x-1+\frac{1}{x-y(x)+2}$$ with initial condition $$ y(0)=0$$ as a part of my homework. The problem is that I cannot understand which type ...
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2answers
60 views

Why this ODE doesn't have a solution?

Consider the following problem: $$u'' + u = \sin t ,\,\, 0 < t < \pi$$ $$u(0) = u(\pi)=0 $$ My book says that this problem doesn't have a solution (classic solution). I don't see how to ...
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4answers
91 views

Laplace Transform & Initial Value Problem

$$ y'' + 4y = \begin{cases} t, & 0 \leq t < 3\\ 1, & 3 \leq t <\infty \end{cases} $$ $$y(0)=0, y'(0)=0$$ I need to find the Laplace transform of the solution of the given IVP above. ...
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3answers
265 views

Does this IVP have a unique solution for all $x \in \mathbb R$

Is $\displaystyle {dy\over dx}=\sin(y)$ with initial conditions $y(X)=Y$ guaranteed to have a unique solution for all $x\in\mathbb R$?
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102 views

Differential equation: finding particular solution when the RHS is in form A/t

Knowing that $$t^2y'' + 3ty' - 3y = 16t$$ for the homogeneous equation has a general solution $$y= c_1t + c_2t^{-3}$$ What is the particular solution? If I divide $t^2$ across the board, I will ...
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3answers
200 views

Reasons For Power Series Solutions of Differential Equations?

A trigonometric function (such as sine or cosine), or some combination thereof, can be the solution of a first order differential equation with constant coefficients. But the solution of a higher ...
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4answers
770 views

Differential equations and family of function solutions

I can't follow what Stewart is doing in his book. I can easily follow his work but his conclusion doesn't make any sense to me. "Show that ever member of the family of functions $$y = ...
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3answers
57 views

What method I should use to solve this differantial equation?

I had this during an exam $$ (x+2) \sin(y) dx + x \cos(y)dy = 0 $$ and it was not given what method I am supposed to use in order to solve this differentiation equation. I have tried to solve it ...
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4answers
115 views

Newtonian Mechanics - Differential equation

If we combine Newton's second law of motion i.e. $F=m\ddot{x}$ and Newton's law of gravity i.e., $$ F=G\frac{mM}{x^2}, $$ where $x$ is distance, we obtain the following equation: ...
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3answers
162 views

Solving the differential equation $ty' + 2y = t^2-t+1$

I wish to solve the following differential equation: $$ty' + 2y = t^2 - t + 1$$ for $t > 0$ and $y(1) = 2$. Seeing as I want to use the method of integrating factors, I divide everything by $t$: ...
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2answers
47 views

Find a solution of $x\frac{dy}{dx} = y^2 -y$ that passes through the points (1/2, 1/2)

I do not understand how my instructor simplified the part marked with red circle. Did he make a mistake? Could anyone help me out here.
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3answers
134 views

top journals in analysis

as an undergraduate I find analysis as my favorite.I want to read journals regarding that. give me top 5 journals in analysis(real,complex)? top 5 journals in differential geometry? and generally some ...
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3answers
312 views

How to solve $y' = \sqrt {x+y+1}$

How does one solve $y' = \sqrt{x+y+1}$? I try substituting $v=x+y+1$ and using substitution methods, but it turned out to be so messy.
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4answers
214 views

Global solution for ODE

Suppose a smooth vector field is given on plane. I want to find a global solution. Is the following procedure ok, or is there a problem? Since the vector field is Lipschitz continuous, we can find a ...
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3answers
105 views

differential equation $u''(x)+u(x) =|\cos(x)| $

I am stuck solving the diff-eq. $u''(x)+u(x) =|\cos(x)| $. How do I find the general solution to this? The homogeneous part is no problem, but how do I deal with the absolute value of the cosine?
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2answers
148 views

Still stuck on treacherous ODE

It has been a while since I posted the question Treacherous Euler-Lagrange equation. I have read the suggested text. But I was told that I shouldn't need Jacobi amplitude function and other beasties ...
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2answers
179 views

Linear ODE, roots of characteristic equation having multiplicity $>1$

I know the method. For a linear homogeneous ordinary differential equation with a root of the characteristic polynomial in $\alpha$ has multiplicity $k$, then $y=x^me^{\alpha x}$ with $m=0,1,\cdots ...
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2answers
492 views

What is the homogeneous problem?

What is the homogeneous problem? What is the purpose of null space of a vector in this context?
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4answers
72 views

Differential Equation: $f'(x) = f(x) (1-f(x))$

I'm lost on the following problem: Find the function f(x) such that f'(x) = f(x)(1-f(x)) and f(0) = 1/7. (Use f for f(x) in your equation). I'm assuming I can write this as: $$ \frac {df}{dx} = ...
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1answer
123 views

If $f(2x)=2xf'(x)$, then find $f(x)$

If $f(x)$ is Analytic functions on $R$,and such $$2xf'(x)=f(2x)$$ Find all $f(x)$ My idea: let $$f(x)=\sum_{n=0}^{\infty}a_{n}x^n$$ so I can't Thank you
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1answer
50 views

Solving a second order differential equation

I'm in the second week of an Elementary Diff. Eq. course and the professor gave us an optional problem that is way beyond the scope of what we've discussed just as a challenge, and I don't know how to ...
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1answer
49 views

Solution of a nonlinear ODE

How can I solve this ODE$$-vU'=2(UU''+(U')^2),$$ where $v$ is a constant. I can see that the right hand side is $(U^2)''$ but is this useful.
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2answers
77 views

Help developing a differential equation

So I'm just studying for my final, and doing some practice DE questions. I have one that asks me to determine a DE given that we have \$100,000 principle being compounded continuously at 5%, but also ...
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2answers
67 views

The solution of $dx+zdy+ydz=0$

How to solve the following differential equation: $$dx+zdy+ydz=0?$$ I know this question seems so easy, but I cannot remember its solution. Thank you for helping.
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3answers
56 views

Definition of Linear Differential Equation

I am a 13 year old self teaching myself Differential Equations from a website and a book, I came across the definition of a Linear Differential Equation but I didn't understand the definition, I ...
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2answers
410 views

Find solution of $\frac {d^2x}{dt^2}=-\sin x$

Problem: Find solution of $$\frac {d^2x}{dt^2}=-\sin x$$ Solution:Integrating both sides with respect to $t$ $$\frac {dx}{dt}=-t\sin x +c_1$$ Again integrating ,we get $$ ...