Find the equations of the trajectories?

[Math10]

Homework Statement

Find the equations of the trajectories of y"+y^3=0.

Homework Equations

None.

The Attempt at a Solution

The Undamped Case:
y"+p(y)=0
v(dv/dy)+p(y)=0
integrate
v^2/2+P(y)=C
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So following the formula above:
The answer I got is v^2/2+y^4/4=C, but the answer in the book says v^2+y^4/4=C. What's wrong?

 

[Simon Bridge]

Did you, blindly, followed a formula?

What makes you think the formula applies in this case?
Did you follow the formula correctly?
Did you check your algebra?
Did you check your arithmetic?

Maybe the book made a typo?