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

[Math10]

Homework Statement

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

Homework Equations

None.

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?

 

[Ray Vickson]

Homework Statement

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

Homework Equations

None.

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?

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!

 

[vela]

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.