Please help me understand and solve the second-order DM: yy" + y = (y')^2

[Dana04]

Hello, please help me to understand and solve the equation:


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

 

[mario99]

The trick here is:

Let [imath]u(y) = y'[/imath]

This is the same as

[imath]u(y(x)) = y'(x)[/imath]