Solve y'+ty=t^3y^3?

1 Answer
Apr 13, 2018

See below.

Explanation:

Making the substitution

y = t/z rArr 1/2t d/(dt)(z^2)-(t^2+1)z^2+t^6=0 now considering

xi = z^2 we have the linear differential equation

1/2 t xi'-(t^2+1) xi+t^6 = 0

now solving for xi

xi = t^2(C_0 e^(t^2)+t^2+1) and then

z = abst sqrt(C_0 e^(t^2)+t^2+1) and finally

y = t/(abs t sqrt(C_0 e^(t^2)+t^2+1))