By the method of separation of variables, solve the equation:
u(subscript tt) + 4u(subscript t) −u(subscript xx) = 5sin(2πx)
for 0 ≤ x ≤ 1, with boundary conditions u(0, t) = u(1, t) = 0 and initial
conditions u(x, 0) = u(subscript t)(x, 0) = 0.
Hello and thank you for posting your question to Brainmass.
The solution ...
The 16-page solution explains what is the general strategy to solve this kind of equations, then goes on and shows in detail how to solve the specific equation, including the methods to solve the ordinary differential equations we need along the way.