# ode

1. ### Solve the Linear ODE of first order first degree

Hi all, I'm stuck with this problem. Please help me to identify which method to use. Attaching the question. Thanks a lot for your help.
2. ### How to solve an ODE to find its solution

Salutations, I have a problem when I approach this ODE: $$\left(\frac{y}{y'}\right)^2+y^2=b^2\left(x-\frac{y}{y'}\right)^2$$ I have done a series of steps as I show in this document: https://drive.google.com/file/d/1Ht4xxUlm7vXqg4S5-wirKwm7vTESU3mU/view?usp=sharing But I'm not...
3. ### Transformation of Equations - What is the deeper thing?

Hi, If you have an ordinary differential equation (or equations), you can transform them under some conditions (integral, linear operator, ...) to algebraic equations. If you have a partial differential equation you may transform it to an ODE. This can be shown "easily" by doing Fourier...
4. ### non linear ode

Hi , i have a question regarding this ode system dx/dt=-y-x^3 ,dy/dt=x ,so it s a question whether this system has a periodic solution respectively an asymptotic equilibrium point and lastely describing the asymptotic behaviour for t goes to infinity of all the solutions . Thanks guys
5. ### Need help for this expression

y''+(3x^2-1/x)y'=A/x Any method can be used to solve this equation? Thanks a lot.
6. ### Question about general substitution for tricky ODE

as you know, many ODE(Ordinary Differential Equation) have explicit solution, but there are also more ODE which doesn't have. Let's think hypothetical need to find solution for a <Stiff ODE> to calculate area below curvature or more generally, to find primitive or anti-derivative function or...
7. ### Ode

Hi everyone, I have been trying to solve this equation, but to no avail. Can you help me? y''+y'/x+y/x^2=0
8. ### Whether to define system as PDE or ODE

Hey everyone. I'm a grad student revising a journal article. Within the article, I layout an equation which describes of population "n(r)" through time. The parameters of this population vary with some variable "r"; however, r does not change with time. When I solve this system (written out...
9. ### Proving general solution for 2nd order ODE

Show that y(t) = A(t^2) + Bt, where A and B are arbitrary constants, is the general solution of the differential equation (t^2)yâ€²â€² âˆ’ 2t yâ€² + 2 y = 0. I got the roots to be r= (1/t)+-(i/t) .... Which I would then plug into the equation involving complex roots which is...
10. ### 2nd Order ODE Problem

I find 2nd Order ODEs quite hard and I've come across this question in my text book but am unsure of how to do it. Can anybody explain step by step how this is done? It would be a huge help considering I've an exam in a few weeks' time on this stuff. :o
11. ### Third order ODE using Euler's method

I'm a bit lost on this one. Is my method below the correct way to set up the ODE? \frac{dQ}{dt}(\frac{d^3Q}{dt^3})=(\frac{dT}{dt})pCp
12. ### Separation of variables, ODE. Is it possible to get a factor t in a solution?

Here's my problem: http://i.imgur.com/XT7Mjw1.png I tried a). But when I look at c), it says u(x,t) = te^{-t}\sin(x) should be a solution and I cannot make that solution; I can only get e^{-t}\sin(x) with the solution I found. So I just need to know: where would a 't' factor come from? By...
13. ### Linear first ODE with variable coefficients

Hi! I used to go about solving linear ODEs with constant and variable coefficients. Upon my knowledge all the times the ones with variable coefficients, the coefficients would be dependent on the one independent variable 'x' say. For example, consider the following ODE: q(x)= A(y) ...
14. ### solving ODE

I need to solve analytically the following second order ODE; W''(X) - f(X)*W(X)=0 WHERE f(X) is an arbitrary known function. Could someone help me as soon as possible?
15. ### Can Anyone help solve this First order ODE?

I'm having a nightmare trying to solve this ODE, If anyone could offer a solution or just insight it would be greatly appreciated. Thank you. All parameters apart from t and x are constant https://www.dropbox.com/s/8cwdnerm5ple9gn/Screenshot_2016-04-07-11-47-27.png?dl=0
16. ### Rearranging ODE's like algebra - please check my understanding

Hello all, I am trying to understand why we can "separate the variables and derivative parts" in ODEs. I have attached a picture of my working out, and on the page I have added numbers at the side, which I will reference now in the typed text to assist what I have done: 1. dy/dx is just the...
17. ### Question about solving ODE

hi guys, Hope it's okay, but I typed out my question to make the math equations more clear. I had a general question about solving ODEs. So as we know, if you have an equation of the form: thanks in advance for your help
18. ### ODE system

Hi guys, I need some help solving the next ODE system: w'+2*U*sin(psi)=0 wv'+2UV*sin(psi)=V'' WU'+(U^2-V^2)*sin(psi)=mTsin(psi)+U'' m,T,psi are constants BCE's: U=V=W=0 @ x=0, U-->0 as x-->infinity, V-->(-1) as x-->infinity Some guidance would be greatly appreciated. shai
19. ### Power series on ODE solution

Dear all, I am a bit rusty on power series expansion, and I am stucked with the following problem. I have the following ODE in terms of two continuous differentiable generic functions u(t) and v(t): \dot{u} = -g_L u + g_D (v(t)-u(t)) + g(t) (E-u) where g_L,g_D,E real and >0 and g(t) is...
20. ### matrix-vector representation for a system of ODE's

I am aiming to explicitly write the matrix-vector representation of this system. yâ€™1 = 5y2 - y1 + y3; yâ€™2 = 3y1 - y2 + t2; yâ€™3 = y3 - ty2 This is what I have so far: [ yâ€™1 ] [ -1 5 1] [ 0] [ yâ€™2 ] = [ 3 -1 0] [ t2] [ yâ€™3 ] [ 0 ? 1] [ ? ] Just not sure how...