Question: Solution - partial differential equation

I'm still a maple beginner and looking for a workable solution to the following problem. I have already solved these "by hand" and would now like to control them.

The following equation should be solved:

diff(u(x, t), t, t)-c^2*(diff(u(x, t), x, x))

The approach function would be for example:

u := a(x)*sin(k1*(-c*t+x))

It would be great if maple could give me the solution again in this example:

solution = -c^2*(d^2*a*sin(k1*(-c*t+x))/dx^2+2*d*a*k1*cos(k1*(-c*t+x))/dx)

How exactly do I do this best?
Thanks a lot!

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