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Find the solution to the two-dimensional wave equation

1. Find the solution to the two-dimensional wave equation

ð²u/ðt²= ð²u/ðx²+ð²u/ðy², 0

boundary conditions u(0,y,t)= u(1,y,t)= u(x,0,t)=u(x,1,t)=0

2. Solve the two-dimensional wave equation for a quarter-circular membrane

The boundary condition is such that u=0 on the entire boundary.

3. Consider Laplace's equation

ð²u/ðt^{2 = c2(}^{ð²u/ðx²+ð²u/ðy²)-k}ðu/ðt with k>0.

a. Give a brief physical interpretation of this equation.

b. Suppose that u(x,y,t)=f(x)g(y)h(t)

What ordinary differential equations are satisfied by f, g, and h?

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Mathematics: Find the solution to the two-dimensional wave equation

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