Consider the system of differential equations in the image where V(x)=x^2+εx^4 with ε≥0: 1. Solve the system if ε = 0. 2.Determine all rest points 3.Proof that (dH)/(dt)=0 with H= (y^2)/2+V(x) 4.Prove that every orbit that does not pass through (0, 0) is periodic.

Consider the system of differential equations in the image where V(x)=x^2+εx^4 with ε≥0: 1. Solve the system if ε = 0. 2.Determine all rest points 3.Proof that (dH)/(dt)=0 with H= (y^2)/2+V(x) 4.Prove that every orbit that does not pass through (0, 0) is periodic.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

100%

Consider the system of differential equations in the image where V(x)=x^2+εx^4 with ε≥0:

1. Solve the system if ε = 0.

2.Determine all rest points

3.Proof that (dH)/(dt)=0 with H= (y^2)/2+V(x)

4.Prove that every orbit that does not pass through (0, 0) is periodic.

If you could provide me with some explanation with the taken steps I would be very thankful, thanks in advance.

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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