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

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4 views

Non-Nondimensionalise of two equations

I'm going over some review for a project I'm doing over the summer and ran into a problem of non-Nondimensionalization. I have not done it in a while and am struggling on how to approach this problem ...
1
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0answers
11 views

what can I say about the solution $y(x)$ of the ODE?

Let $y:\mathbb R\to \mathbb R$ be differentiable and satisfy the ODE: $$\frac{dy}{dx} =f(y),x\in\mathbb R$$ $$y(0)=y(1)=0$$ where $f:\mathbb R\to \mathbb R$ is a Lipschitz continuous function. Then ...
-2
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2answers
26 views

Solving a Differential Equation with strange initial conditions

I am not really sure how to work with these initial value conditions. Thank you for the help. This is the problem: $y"-y=0$, $y(0)=0$, $y(1)=-4$
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0answers
9 views

Uniqueness of a solution of differential equation

I have been trying to deal with this differential equation $y'=\frac{2}{t}y+t^2e^t, y(0)=1, 1\leq t\leq2$, and the problem asks to show that the solution is unique. I think this shouldn't be ...
0
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0answers
18 views

Help solving a Differential Equation?

dx/dt= x-4y dy/dt=4x=7y I found the eigenvalue to be -3 and the general solution to be $x=e^{3t} x_{initial} +te^{3t}(-2x-7y)$ and $y= e^{3t} y_{initial}+ te^{3t} (-x+y)$ Determine the particular ...
-3
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0answers
27 views

Solve the following differential equation

Solve the following differential equation: A detailed, step by step solution will be greatly appreciated! $$ \frac{d^2y}{dt^2} +y=\tan t $$
-2
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0answers
11 views

Solve the following differential equation

Solve the following differential equation: d^2y/dt^2+5dy/dt-14y=-14t^2+10t+30 initial conditions: y(0)=6, y'(0)=11
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0answers
19 views

Solve $x(x-1)y''+6x^2y'+3y=0$ using Frobenius's Method

Solve $x(x-1)y''+6x^2y'+3y=0$ using Frobenius's Method I can't solve this ODE. How can I get first two term? and indicial equation is also very confusing. I can solve two term recurrence ...
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2answers
17 views

Differential Equations: Recursive Functions

Functions I have some familiarity with look so, $y^\prime(x) = \tan(x+2)$: straightforward expression of the first derivative of y as a function of x. But say I have a function, $y^\prime(x) = ...
2
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2answers
24 views

Short question about definition in ODEs

Hello I just have a short question about a remark made in my first class of intro ODE. My Professor was just motivating with a simple example, he wrote, $$\frac{dy}{dx}=y(x)$$ So of course it was ...
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0answers
17 views

How can I solve this ODE with nonconstant coefficient?

$x(1-x)f''(x) - \lambda f(x) = 0$, where $\lambda$ is just any constant. So far, I've just tried guessing certain functional forms, but none of them seem to work.
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1answer
21 views

solving second order linear differential equation

Can somebody please show me how to solve the following differential equation: $$ a\ddot{x} + b\dot{x} = c $$ given these initial conditions $x(0) = 2$, $\dot{x}(0) = 0.5$ and $a = 4, b = 1.5$ First ...
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0answers
12 views

differential equations, elliptic equation

Solve the problem Can this be solved analytically or only numerically? What method should be used?
2
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1answer
16 views

Second Order Non-Linear Ordinary Differential Equation

I have the equation $$x_{tt}+cx_t+x=x^2$$ where $c$ is constant and $x=x(t)$. If the $x^2$ wasn't on the right hand side of the equation then I could solve this easily by the method of ...
3
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3answers
36 views

Equation for dye in pool

I recently began my first course in intro do ordinary differential equations. The textbook recommended for the class is "Elementary Differential Equations and Boundary Value problems, 10th edition" by ...
0
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1answer
19 views

Exact Ordinary Differential Equation [on hold]

Find the sufficient condition for the differential equation $$M(x,y)dx+N(x,y)dy=0$$ to have an integrating factor as a function of $x+y$. What will be the integrating factor in that case?
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2answers
15 views

Finding the general solution to a non-homogeneous ordinary differential equation

How do I go about solving this question?: Find the general solution of the non-homogeneous ODE $y''+\frac 12y'+\frac{1}{16}y=cos(\frac x4)$. Solving the homogeneous equation, I get the real root ...
2
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2answers
49 views

I need a Hint on this Differential equation

Let $f$ and $g$ be two real functions, and we have $$ (f*g)(t)= \int_0^tf(s)g(t-s) \, ds $$ we have the following equation $$y'+ay=f(t) $$ where a is a constant and f is a function -/ prove that if ...
1
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0answers
16 views

Integral of a funtion avoiding hypergeometric functions

I'm solving the following differential equation: $$uy''(u)+\gamma y'(u)+\frac{1}{u(1-u)}=0,~~\gamma=constant$$ For that, I transform this equation into a first orer one: $$uf'(u)+\gamma ...
1
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0answers
22 views

Reduce PDE to ODE

Maybe you don't want to check all the details, but could look at a few equations here. Would you mind leaving a comment that you at least some part looks okay?- This way, I know that at least somebody ...
1
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1answer
31 views

How to solve this differential equation? $2xy\frac{dx}{dy}+x-y^2=0$ [on hold]

I ask for help with this one: $2xy\frac{dx}{dy}+x-y^2=0$
3
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1answer
33 views

Solving an SDE: $dX=-Xdt+e^{-t}dW$

I have the following problem which comes with the solution, but I am unable to obtain the solution... Any help would be greatly appreciated - I am preparing for finals :( Thanks a lot! The SDE that I ...
3
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0answers
13 views

Can we derive the PDE followed by a marginal transition probability density?

A pair of correlated stochastic processes follow the SDEs \begin{align} dX_t&=a(t,X_t)\,b(t,Y_t)\,dt+c(t,X_t)\,d(t,Y_t)\,dW_t, &&X_0=\bar{x}\\ dY_t&=f(t,Y_t)\,dt+g(t,Y_t)\,dZ_t, ...
2
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1answer
37 views

General solution for differential equation

I have the following differential equation ; $$\frac{dx\left(t\right)}{dt}=ay\left(t\right)-bx\left(t\right)$$ where $a$ and $b$ are positive constant terms. $t$ indicates time. I am trying to ...
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2answers
30 views

Is the following Differential Equation undefined for given values of X & Y?

I have been presented with the following differential equation which I'm asked to solve, where $y=0$ when $x=\pi$. $$(y+1)\sin x\frac{dy}{dx} = (y^2+1)\tan^2x$$ I notice that $(y^2+1)$ may be ...
2
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1answer
28 views

find $\lambda$ such that the integral has a solution.

I have the integral equation: $u(x) = f(x) + \lambda \int_0^{\frac{1}{2}}u(y)dy$ I have to find $\lambda$ such that the integral has a solution. How to approach such problems?
1
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1answer
19 views

Finding the characteristic timescale of a first-order nonlinear ODE

I know that to find the timescale of a first order linear equation $$\frac{dX(t)}{dt} + aX(t) = b$$ you just take the inverse of the integrating factor, so $$t_x = \frac{1}{a}$$ Henning and ...
1
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1answer
39 views

Trouble with derivatives using Newton-Raphson in MatLab

I'm finding it very difficult to get my head around how best to express the following system of equations in MatLab in order to solve it. The equations come from Von Karman's similarity solution to ...
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0answers
4 views

Can low order methods for solving ODEs be non-stiff if high order methods are stiff? [on hold]

I'm trying to solve a an ODE system (1000 equations) on Matlab. I want to check the difference between the solution provided by the ODE45 solver of Matlab and an implementation of the same equations ...
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0answers
22 views

Laplace Transformation : differential equations

Dont know how to proceed further. Please Help me guys
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0answers
27 views

ordin differential equation [on hold]

i will like to get the answers please... please thanks for helping me
1
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1answer
30 views

Proving dense subset in metric space

Could anyone help with the following basic metric space problem? Show that $A$ is dense in $X$ if and only if the only closed set containing $A$ is $X$. I know the general idea is to take Cauchy ...
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0answers
20 views

Converting second order system into first order system (ODE)

The second order equation $\frac{d^2\vec{x}}{dt^2} = A\vec{x}\ + \vec{g}(t)$ models an earthquake's effect on a 7-story building. Let $x_j(t)$ be the displacement of the $j$th floor with respect to ...
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0answers
9 views

Starting on a sketch of unit function

I have the following unit step function: u2(t)+1-u1(t) The constant is confusing me, can you help get me started?
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0answers
11 views

Derive stochastic differential equation of Y(t) = 2 + t + e^(W(t)) [on hold]

How do I derive the stochastic differential equation of $Y(t) = 2 + t + e^{W(t)}$ ?
1
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1answer
35 views

Particular integral for $x\sin(1-x)$?

$$y''+y=x\sin(1-x)$$ I have got that the solution to the homogenous case is $$y = A\sin(x)+B\cos(x),$$ but what about the inhomogenous case? Which particular integral do I use? I have tried ...
2
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2answers
21 views

Finding all functions f(y) such that a differential equation becomes exact

Can somebody help me with this question? Find all functions f(y) for which the differential equation becomes exact: $$ x^2 + \frac {f(y)}{xy} + ln |xy| \frac {dy}{dx} = 0 $$ If I set $P(x,y)=x^2 + ...
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2answers
24 views

Converting a second order n x n system into a first order 2n x 2n system

Say I have the following second order 7 x 7 system of equations: $x_1'' = 10(x_2- x_1- 1)$ $x_2'' = 10(x_3- 2x_2+ x_1)$ $x_3'' = 10(x_4- 2x_3+ x_2)$ $x_4'' = 10(x_5- 2x_4+ x_3)$ $x_5'' = 10(x_6- ...
4
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0answers
28 views

Analytic approximation of $\ddot x+\gamma sign(\dot x)+x=0$

I am trying to find an analytic approximation to this non-linear differential equation. $$ \ddot x+\gamma sign(\dot x)+x=0 $$ $\gamma$ is a very small parameter. The solution I am getting is $$ ...
3
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2answers
38 views

Dynamical System transformation

How can the system $$\frac{dx}{dt}=-y+\epsilon x(x^2+y^2)$$$$\frac{dy}{ dt}=x+\epsilon y(x^2+y^2)$$ be transformed into $$\frac{dr}{dt}=\epsilon r^3$$ $$\frac{d\theta}{dt}=1$$ via polar coordinates? ...
0
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1answer
42 views

Variational differentional equations

For $f \in C^1(D)$, $D$ compact, there exists unique solutions (locally) for $\dot{y} = f(t,y)$, $y(t_0) = y_0$. We denote the solution with $y(t;t_0,y_0)$. Let $G(t;t_0,y_0) := ...
1
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1answer
20 views

Solving IVP by Laplace transform

I'm trying to solve an IVP with non-constant coefficients $$ y'' + 3ty' - 6y = 1, \quad y(0) = 0, \; y'(0) = 0 $$ Taking the Laplace yields $$ s^2Y + 3(Y + sY') - 6Y = \frac{1}{s}$$ $$ Y' + ...
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2answers
49 views

Help me with understanding this solution

$$2x^4yy'+y^4=4x^6$$ The way my teacher did it is: First, he made a substitution: $y=z^m$ $y'=mz^{m-1}z'$ $$2x^4 z^m mz^{m-1} z'+z^{4m}=4x^6$$ ...
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1answer
16 views

What really is a path-ordered exponential?

In some texts about gauge theories in Physics I've found one object called a path-ordered exponential which I'm not sure what it means. As I understood, the idea is as follows: let $G$ be a Lie group ...
0
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4answers
41 views

How to solve $y''(x)+\frac{1}{x}y'(x) = 0$?

I'm solving a differential equation by using reduction of order, which results in solving: $$y''(x)+\frac{1}{x}y'(x) = 0$$ I have found $y(x) = \ln x + C$ to be valid solution, by guessing... ...
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0answers
15 views

What is a “limit circle boundary condition”?

I came across the notion in an article on differential equations and I did not find any satisfactory answer on it as yet. In more detail, it was concerning the differential operator ...
2
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1answer
26 views

Transforming integral equation to differential equation

I was given the task to find all continuous functions that satisfy the following equation: $$x \int_0^x {y }dx=(x+1) \int_0^x{xy}dx$$ I am quite new to differential equations so my first thought ...
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1answer
27 views

Modeling a planes flight

my text book for differential equations has a nice applied 'project'/investigation that I have been working through over the weekend (this is not a homework question I just thought it may be ...
3
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2answers
25 views

How to solve this simple yet troublesome differential equation

$\frac{d^2y}{dx^2}-2\cdot \frac{dy}{dx}=0$ I am a newbie to differential equations, and I tried to separate variables, but had no success. MY course only covered first order equations, but I am ...
2
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3answers
26 views

Finding particular solution to $y'' + 2y' - 8y = e^{2x} $

$$y'' + 2y' - 8y = e^{2x} $$ How do I find the particular solution? I tried setting: $y = Ae^{2x} => y' = 2Ae^{2x} => y''= 4Ae^{2x}$ If I substitute I get: $4Ae^{2x} + 4Ae^{2x} - 8Ae^{2x} = ...