# Homework Help: Find the equations of the trajectories of y"+y^3=0

1. Feb 13, 2015

### Math10

1. The problem statement, all variables and given/known data
Find the equations of the trajectories of y"+y^3=0.

2. Relevant equations
None.

3. The attempt at a solution
y"+p(y)=0
v(dv/dy)+p(y)=0
integrate
v^2/2+P(y)=C
so I got v^2/2+y^4/4=C. Is v^2/2+y^4/4=C the correct answer?

2. Feb 13, 2015

### Ray Vickson

Substitute it into the DE and check to see if it works. You can do it just as easily as we can, and (as I have said before), doing your own checking first is a good habit to develop. You won't be able to ask for help when you write an exam!

3. Feb 13, 2015

### vela

Staff Emeritus
Nope. You're looking for an expression where y is expressed as a function of x (or whatever your independent variable is). Right now, what you have is
$$\frac 12 (y')^2 = C - \frac 14 y^4.$$ You need to solve that differential equation now.