Is ψ(t,0,0) = sin(2πt) a Solution to This Differential Equation?

[DaVikes84]

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 can't 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.

 

[pasmith]

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 can't 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 $$\psi' + \psi^3 - 2\psi = \sin^3(2\pi t) - 2\sin(2\pi t) + 2\pi\sin(2\pi t)$$
which, unfortunately, is not the case; there needs to be $2\pi\cos(2\pi t)$ on the right instead of $2\pi \sin(2\pi t)$ for that to work.