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

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2
votes
0answers
12 views

clarification of a doubt over a defined result in ODE

I was going through the topic of Wronskian in ODE came up with the following result: I have a little doubt. Can we say the same if we interchange $y_1$ and $y_2$ i.e. between consecutive zeroes of ...
0
votes
2answers
25 views

Find value of $xy\sqrt{y^2 - x^2}$ for the given differential equation.

If $(y^3 - 2x^2y)dx + (2xy^2 - x^3)dy = 0 $ , then prove that the value of $xy\sqrt{y^2 - x^2}$ is a constant. This is what I've tried : $$ y(y^2 - 2x^2) dx + x(2y^2 - x^2) dy = 0 \\ ...
2
votes
1answer
20 views

Use of Laplace transform to solve initial value problem.

--Short Explanation: I have to say I am going crazy with this problem as it does not give me the same as the suggested solution in the book: Problem: $y''-7y'+10y=9\cos{t}+7\sin{t}$ $y(0)=5$, ...
-1
votes
1answer
18 views

Looking for help in regard to Series solutions with ordinary points (ODE)

I have a question that is in regard to the final answers/answer that one is to get when solving some ODE questions via series. I am having some confusion on what if I am doing is correct/ why it is or ...
2
votes
1answer
13 views

Third-order differential equation with initial values using Euler method

The problem I have is the initial value problem $$y''' = x + y$$ with $$ y(1) = 3, y'(1) = 2, y''(1) = 1$$ that should be solved with Eulers method using the step length, $h = \frac{1}{2}$. The ...
1
vote
1answer
17 views

Heat Equation on $[0,l]$ with Neumann boundary conditions

I was reading the following pdf about the heat equation on an interval $[0,l]$ with Neumann conditions, http://texas.math.ttu.edu/~gilliam/fall03/m4354_f03/heat_N_web/heat_ex_homo_neum.pdf i.e. ...
2
votes
0answers
26 views

solving second order non-homogeneous differential equation 3

Help me to solve this non-homogeneous differential equation : $ y''+y=\tan x $ $ 0<x<\dfrac{\pi}{2} $ I could reach to $y_{c}=c_{1}\cos x + c_{2}\sin x$ but particular solution is where I ...
0
votes
2answers
30 views

Differentiate $\sum_j\sum_i a(i,j)b(i,j)$ wrt $a(i,j)$

How do you differentiate a sum of a variable, wrt that variable, e.g. Find $\frac{dc}{da(i,j)}$ where $c = \sum_j\sum_i a(i,j)b(i,j)$. Context: I'm trying to find the jacobian.
1
vote
2answers
37 views

Solving differential equation $x'=\frac{x+2t}{x-t}$

I am trying to solve the following differential equation: $$x'=\frac{x+2t}{x-t}$$ with initial value condition: $x(1)=2$ This is what I have so far: Substitution: $u=\frac{x}{t}$ $$\implies ...
0
votes
1answer
35 views

Differentiate this power series

I am working on a problem which involves the differentiation of a power series. I know that that the following holds. Let $R$ be the radius of convergence of the power series $\sum_{n = 0}^\infty ...
1
vote
2answers
46 views

second order differential equation 1

I tried to solve this equation and reached to below answer but I think it needs to some recheck.please help me to get sure of this differential equation : $ 2y^{2}y''+2y(y')^{2}=1 $ my guess for this ...
0
votes
2answers
48 views

solving differential equation 1

please help me to solve this differential equation : $$ y'= \frac{x^2+3y^2}{2xy} $$ I found this as answer but I'm not sure : $$ \ln|x|=\ln\left| \frac{y^2}{x^2}+1\right|+c $$
0
votes
2answers
29 views

First order nonlinear ordinary differential equations

In my exercise I am stuck in a problem given below: $\ln\left(\frac{dy}{dx} \right) = x-y+1$ Although I could solve it if it was a linear equations. But ln() is a nightmare for me. Can anyone help me ...
4
votes
2answers
70 views

Solving differential equation $x''(t)=x^6$.

Solve the following differential equation $$x''(t)=x^6(t)$$ If I had $x'(t)$ instead of $x''(t)$ the exercise would have been easier for me. I would appreciate some help with this problem. Thank ...
0
votes
1answer
9 views

Synchronization of Rossler system - the Rossler Attractor

I am studying synchronization of Rossler system given by the following set of two linear ODEs and one nonlinear ODE: $\dot{x_1} = -x_2 - x_3$ $\dot{x_2} = x_1 + ax_2$ $\dot{x_3} = c + x_3(x_1 - b)$ ...
-4
votes
0answers
31 views

Elliptic Partial differential equation [on hold]

I could not understand the proof of Theorem 8.24 in Gilberg Trudinger's book. They Stated that it follows from Theorems 8.17 and 8.22. One more thing that how can i apply Lemma 8.23 to conclude the ...
0
votes
2answers
13 views

How to show that the general solution has the form:

We have an ode as such: $y'' + (sint)y'+t^2y=0$ Also, we know that $y_1$ and $y_2$ are linearly independent solutions. How to show that the general solution has the form: $y=c_1y_1+c_2y_2$ where ...
0
votes
2answers
40 views

Particular solution of the differential equation $ y' + (2/3)y = 1-(1/2)t, y(0)= y_0 $

I have this particular differential equation: $$ y'+(2/3)y = 1 - 1/2t, y(0) = y_0$$ I have to find the specific value $y_0$ where the solution touches t axis, but it does not cross it. I found the ...
-2
votes
0answers
20 views

Differential equations??? [on hold]

Two tanks of salt solution are connected to one another, with Tank 1 containing 30 gal of water and 25 g of salt and Tank 2 containing 20 gal of water and 15 oz of salt. Water with 1 g/gal of salt ...
-1
votes
1answer
22 views

Use of undetermined coefficients issue

I'm given the problem $$y'' + 4y' = t$$ and asked to solve for y. I compute the general solution (using the characteristic equation) to be $$c_1 + c_2e^{-4t}\ ,$$ which I am pretty sure is correct. ...
0
votes
1answer
33 views

Solve the system of differential equations

I plan on adding more into later just a bit stuck, researching it at the moment. Solve the system of differential equations $$\begin{bmatrix} x'\\y' \end{bmatrix} - \begin{bmatrix} -11&15\\ ...
1
vote
2answers
29 views

Second order differential equations where rhs $= 6e^2\cos(3x)$

Solve the differrential equation $$y'' - 4y' + 13y' = 6e^{2x}\cos(3x)$$ where $y(0)=3$ and $y'(0)=-8$ I think we start like... For the homogenous case $$\lambda^2 -4\lambda + 13 = 0 $$ ...
1
vote
2answers
24 views

Finding particular solution to inhomogeneous system of differential equations

I am asked to find the general solution set of the following system of differential equations: $$\begin{cases} x' = 3x -2y-2 \\ y' = 6x-4y-1 \end{cases} $$ I found the general solution set of the ...
0
votes
4answers
39 views

First order differential equation: did i solve this equation right

So i'm trying to solve: $$x^2\frac{dy}{dx} + 2xy = y^3$$ I'm given this differential equation, that Bernoulli equation: $$\frac{dy}{dx} + p(x)y = q(x)y^{n} $$ I think i've solved it and ...
2
votes
0answers
31 views

upper bound of a differential equation solution

Let $A(t)$ be a bounded singular values matrix that is function of time, and $f(t)$ and $L^\infty$ function of time. And consider the ODE $$ \dot x = A(t) x + f(t) $$ How we can describe qualitatively ...
0
votes
0answers
22 views

Newton backward and forward interpolation (for ODEs) intuition.

For Newton's backward and forward formulas, I understand everything algebraically, but can someone please explain me this formula intuitively, especially intuition how "powers of the forward ...
0
votes
0answers
8 views

Homogeneous and Nonhomogeneous ODEs - where the name comes from?

Why differential equations can be called Homogeneous and Nonhomogeneous? I understand equations behind these names, but where the word "homogeneous" comes from?
0
votes
0answers
32 views

upper bound of an $L^\infty$ function's derivative

Consider a function $u:\mathbb{R} \longrightarrow \mathbb{R}^n$ that is essentially bounded, i.e., $u \in L^\infty$. There is an upper bound of its derivative? I think there is not allways ( i.g. ...
0
votes
0answers
25 views

Trying to use the method “Stiff” (Rosenbrock method implementation) from the book “Numerical Recipes in C”.

The program is compilable but I don't think it works correctly. According to the book, we need also method "odeint" for adaptive stepsize adjustment and fully implement Rosenbrock method. I used the ...
-1
votes
0answers
30 views

Solving Differential equation using Frobenius Method [on hold]

I want to solve a differential equation using the Frobenius method but unable to do it.Please anyone solve this for me.The equation is $$x(1+x)y''+3xy'+y=0$$
1
vote
1answer
37 views

First order differential equation: how do I prove that $u$ satisfies the differential equation

So I'm given this differential equation, that Bernoulli equation: $$\frac{dy}{dx} + p(x)y = q(x)y^{n} $$ now it says: Show that if $y$ is the solution of the above Bernoulli differential ...
-1
votes
0answers
20 views

Applied mathematics for Clinical Medicine [on hold]

I'm a medical graduate, looking for advice/help on a project I would like to start. I would like to use applied mathematics to deconstruct the medical SOAP note into data sets that can be reproduced ...
0
votes
1answer
14 views

Need help with Laplace transform of piecewise /step functions

Hi I am having trouble figuring out how to calculate the laplace transform for $f(t)$ where $$f(t)= \begin{cases} e^{4t} & \text{if $ 0 \lt t \lt 2 $} \\ 1 & \text{if $ t \gt 2 $} ...
0
votes
0answers
32 views

Some results on Robin boundary conditions

I have the following boundary problem $$ (P): \left\{\begin{array}{l} y''(t) = p(t)\, y'(t) + q(t)\, y(t) + r(t),\\ y(t_1) = \alpha, \\ y'(t_2)+\gamma \cdot y(t_2) = \beta, \end{array}\right. $$ ...
-1
votes
0answers
26 views

Differential Equation ODE. [on hold]

Hello I have a problem with this differentials equations of first-order, im trying to do it with ode23 and ode23s. The differentials equations are the next one: y'+3y+z=0 z'-y+z=0 with this initial ...
1
vote
0answers
16 views

Why is this ODE solution only unique in either $(-\infty,0]$ or $[0,+\infty)$ and not in $\mathbb{R}$

Consider the following ODE: $$y'(t)=f(t,y)=e^{-t}+\log(1+y^2)$$ $$y(0)=0$$ You can clearly see the function is continuous on both variables, and the partial derivative with respect to $y$ is: ...
-3
votes
2answers
49 views

Differential equation $y''-4y = e^{-x}$ [on hold]

I need help with the following differential equation: $$y''-4y = e^{-x}$$ (no initial conditions given) Any help is appreciated.
-1
votes
0answers
16 views

Examples of ODEs with 3-dimensional function

I'm trying to test a numerical method program and I need some test cases, i.e. ordinary differential equations. I found some but in these examples the original Y funtion is unknown. I want to check if ...
5
votes
2answers
41 views

System of 3 differential equations

I'm trying to solve this system $$ \begin{align} x'&=x-3y+3z\\ y'&=-2x-6y+13z\\ z'&=-x-4y+8z \end{align} $$ must be reduced to a single equation I tried to express the x 3 and substitute ...
3
votes
1answer
36 views

problems with differential equation

i have problems solving eq. $$ u + \log(u-1) = \log (x); \quad u= \frac{y}{x}$$ which comes from solving diff equation $$x \frac{dy}{dx} - y= x\frac{y-x}{y+x}$$ any hints? thanks in advance
7
votes
4answers
288 views

solution to differential equation from deriving power series

Find the solution of the differential equation $$y'= 2xy$$ statisfying $y(0)=1$, by assuming that it can be written as a power series of the form $$ y(x)=\sum_{n=0}^\infty a_nx^n.$$ Im advised to ...
0
votes
2answers
16 views

A general solution of a partial differential equation with $f(x,y)$

I need to find a general solution to such a PDE: $$u_x-u_y=f(x,y)$$ I am able to find a solution if $f(x,y)=0$ or $f(x,y)=u$. But I have no idea how to get the general solution. Has anybody got any ...
1
vote
1answer
22 views

Differential equation where one solution induces a set of solutions

Consider a differential equation of the form: $$y' = f\left(\frac{y}{x}\right);\space\space\space x ≠ 0$$ where $f$ is any continuous function. I want to show that if $y(x)$ solves this equation, ...
0
votes
3answers
42 views

linearly independent (Linear algebra)

Show graphically that $y_1(x)=x^2$ and $y_2(x)=x|x|$ are linearly independent on $-\infty$ to $\infty$ but Wronskian vanishes at every point. The Wronskian is $$W = ...
2
votes
2answers
177 views

Laplace operator defined on a Sobolev space

Consider the Laplace operator $$A:W^{2,2}(\mathbb{R})\to L^2(\mathbb{R})\;\;\\A u = -u^{\prime \prime}$$ I want to know why this operator is closed (I'm using the closed graph theorem): Let ...
-2
votes
0answers
33 views

Differential equation with steps [on hold]

What steps are involved in solving this differential equation? I found the answer at Wolfram, but it didn't show me how to get to the answer. $$y''+ y = \sqrt{x+y+1}$$
1
vote
1answer
22 views

How do we deduce that the initial value problem has always a unique solution?

Theorem - General solution of $y''+p(x)y'+q(x)y=0, x \in I (\star)$ Let $y_1, y_2$ be linearly independent solutions of $(\star)$ in an interval $I$. Then if $y$ is a solution of $(\star)$ in $I$, ...
-3
votes
0answers
45 views

solve differential equation of $y''+y = \sqrt{x+y+1}$ [on hold]

I tried to solve this differential equation with no result, I even tried http://www.wolframalpha.com/ that showed no steps .. any help ?
0
votes
0answers
22 views

wave equation on a circular domain

Consider the wave equation for the displacement $$\text{u(r,$\theta $,t)}$$ in a circular domain $$\text{0 $<$ r $<$ a, -$\pi $ $<$ $\theta $ $<$ $\pi $}$$ How do I use the separation ...
3
votes
3answers
76 views

a linear differential equation with periodic coefficients

Let $$y' = a(x) y + b(x)$$ be a linear differential equation with continuous, periodic coefficients $a, b: \mathbb{R} \to \mathbb{R}$ that both have a period of $T > 0$. Also, we assume that ...