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## Homework Statement

Given: y'' - y - (y^3) = 0 (equation 1)

E = (1/2)(v^2) - (1/2)(y^2) - (1/4)(y^4) (equation 2)

v = y'

i. Show that E is a conserved quanitity

ii. Find all the solutions with E = 0

**2. The attempt at a solution**

I'm not sure how to show a quantity is being conserved. In fact, I have no idea how to begin this problem!!!! Does anybody have some information to help me just get started?

I solved equation 2 for v = (E + y^2 + (1/2)y^4)^(1/2). I realize I can integrate and solve for y(t) but it is really very messy and I don't see how doing so can immediately benefit me.

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