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## Main Question or Discussion Point

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

dx/dt = -x

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.

dx/dt = -x

^{3}+ 2*x + sin^{3}(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.