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## 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?