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+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?