Differential Equation Question

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I need to prove that the solution of this differential equation:

dx/dt = -x3 + 2*x + sin3(2*pi*t) - 2*sin(2*pi*t) + 2*pi*sin(2*pi*t)

has the solution:

ψ(t,0,0) = sin(2*pi*t)

I know that I need to get all of the x's on one side and the t's on the other then integrate, but I cant figure out how to get the x's and t's together. Is there a little trick or something to solving this?

Thanks a lot.
 

Answers and Replies

  • #2
pasmith
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I need to prove that the solution of this differential equation:

dx/dt = -x3 + 2*x + sin3(2*pi*t) - 2*sin(2*pi*t) + 2*pi*sin(2*pi*t)

has the solution:

ψ(t,0,0) = sin(2*pi*t)

I know that I need to get all of the x's on one side and the t's on the other then integrate, but I cant figure out how to get the x's and t's together. Is there a little trick or something to solving this?

Thanks a lot.
No integration is necessary. All you would need to do is show that [tex]\psi' + \psi^3 - 2\psi = \sin^3(2\pi t) - 2\sin(2\pi t) + 2\pi\sin(2\pi t)[/tex]
which, unfortunately, is not the case; there needs to be [itex]2\pi\cos(2\pi t)[/itex] on the right instead of [itex]2\pi \sin(2\pi t)[/itex] for that to work.
 

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