Question

y' + (1/4)y = -t^2 e^t y^5

Answer 1

let z = y^(-4) maybe

Answer 2

\[y' + (1/4)y = -t^2 e^t y^5\]
\[y'y^{-5} + (1/4)y^{-4} = -t^2 e^t \]
\[z=y^{-4}~:~z' = -4y'y^{-5}\]
\[-\frac14 z'+ (1/4)~z = -t^2 e^t \]

Answer 3

solve for z to determine y

Answer 4

to clean it up some:
\[z'-z = 4t^2 e^t\]