Question

y'=t-1+y^2 . . . How to solve? Cannot be linear first order ODE due to the y^2, can it?

Answer 1

t=-y^2+y+1

Answer 2

Another way of writing it is
-t-y^2+y+1 = 0

Answer 3

Try letting:\[y(t) = t \eta(t) \implies \dot y = \eta(t) + t \dot{\eta}(t) \implies \eta(t)+t \dot \eta (t) = t - 1 + t^2 \eta^2(t)\]
From here you could try laplace transforms and get something then convert back?

Answer 4

I can assume that this is a parabola

Answer 5

blast234, what are you talking about?

Answer 6

I think I did it wrong I did not watch out for the ' in the Y

Answer 7

My bad XD

Answer 8

In general there is no way to solve non-linear ODEs every time, I just threw out a technique I've seen used.