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Partial Differential Equation Boundary Conditions

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Find the general solution of the wave equation U(tt) = U(xx) subject to the boundary conditions u(0,t) = u(1,t) = 0.

Then find the unique solution of the wave equation subject to the initial conditions:

u(x,0) = 2sin3pix and ut(x,0) = 5 sinpix


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The expert examines partial differential equation boundary conditions.

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The equation is:
The boundary conditions are:
And initial conditions:
We start with separating the equation by defining:
The functions are completely independent of each other and therefore:

Plugging this back into (1.1) and dividing by we obtain:

Each side of (1.7) is completely independent of the other side. The left hand side is a function of t while the right hand side is a function of x. Since (1.7) must ...

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