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## Homework Statement

Solve the following differential equation:

## Homework Equations

2 y (y'')^2 + 2 y y''' y' -2 (y')^2 y'' = - (y')^2

## The Attempt at a Solution

I don't know if the following is useful, but if you divide both sides by y^2, the LHS of the above becomes:

(2 y (y'')^2 + 2 y y''' y' -2 (y')^2 y'')/y^2 = ( (2 y' y'')/y )'

Which means the equation to solve is;

( (2 y' y'')/y )' = - (y')^2