Question: solve u(x, t)= sin sin (WAVE FUNCTION OF 1 DIMENSION) ( ^2 / t^2 = c^2 *(^2 / x^2) ) with BCs and ICs using

solve u(x, t)= sin sin (WAVE FUNCTION OF 1 DIMENSION) ( ^2 / t^2 = c^2 *(^2 / x^2) )

with BCs and ICs using separating variables.Please show the details and how to identify the eigenfunctions.

a) BCs: (0, ) = 0 , (0, ) / x = 0

b) ICs: (, 0) = sin ((3*pi*x)/2L) , (, 0) / x = 0

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