First order differential equation with substitution

[kaitamasaki]

Homework Statement

t^2 y' + 4ty - y^3 = 0

Homework Equations

Hint was given in the question: substitute with v = y^-2

The Attempt at a Solution

Dividing by t^2 and isolating y':
t^2 y' = y^3 - 4ty
y' = y^3 / t^2 - 4y/t

dv/dt = 0
y = v^(-1/2)
dy/dt = (-1/2)v^(-3/2) v'

so y' = dy/dt = (-1/2)v^(-3/2) v' = v^(-3/2) - 4t(v^(-1/2))

But after playing with algebra I cannot separate v and t,
I end up with;
dv/dt - 8v/t = -2/t^2
Where v' = dv/dt

How should I have approached this problem?

 

[tiny-tim]

hi kaitamasaki!

(try using the X² icon just above the Reply box )

Dividing by t^2 …

why t² ?

try dividing by y³ ​

 

[kaitamasaki]

Oh gee can't believe I missed that
Had to use integrating factor after