Find solution of initial value problem  1st order nonlinear ODEby mihyaeru Tags: 2nd semester, math courses, ode, ode first order help, ode non linear 

#1
Jun2311, 02:25 PM

P: 4

Hey,
we have to solve the following problem for our ODE class. 1. The problem statement, all variables and given/known data Find the solution of the initial value problem dx/dt = (x^2 + t*x  t^2)/t^2 with t≠0 , x(t_0) = x_0 Describe the (maximal) domain of definition of the solution. 3. The attempt at a solution Well, I know that this is a 1st order nonlinear ODE. Unfortunately I got no clue how to deal them. I tried this: dx/dt = (x^2 + t*x  t^2)/t^2 = x^2/t^2 + x/t 1 Now substitute: u = x/t > x=ut , x'=u't+u Therefore we get: u't+u = u^2+u1 t* du/dt +u = u^2+u1 //u t* du/dt = u^2 1 0= t*u' u^2 +1 which is my dead end. Is the idea ok? What could I do? Kind regards, mihyaeru PS: How can i insert a fraction? 



#2
Jun2311, 02:37 PM

P: 4

I just noticed that we might be able to solve this via applying the Riccati equation????




#3
Jun2311, 03:41 PM

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#4
Jun2311, 04:09 PM

P: 4

Find solution of initial value problem  1st order nonlinear ODE
As far as I know it is a separation of variables case, iff there would be no t in front of the du/dt. Or no 1.
You think of the solution du / (u^2 1) = dt / t , don't you? But anyway thanks for your answer =) 



#5
Jun2311, 09:42 PM

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#6
Jun2411, 02:14 AM

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