- #1
mihyaeru
- 4
- 0
Hey,
we have to solve the following problem for our ODE class.
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.
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+u-1
t* du/dt +u = u^2+u-1 //-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?
we have to solve the following problem for our ODE class.
Homework Statement
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.
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+u-1
t* du/dt +u = u^2+u-1 //-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?