The 1D Wave Equation on an Interval;

Homogeneous Boundary Conditions

Homogeneous Dirichlet Boundary Conditions
$cos(t)\; sin(x)$	$cos(2t)\; sin(2x)$	$cos(3\; t)\; sin(3x)$	$cos(4\; t)\; sin(4x)$
Homogeneous Neumann Boundary Conditions
$1$	$cos(\; t)\; cos(x)$	$cos(2\; t)\; cos(2x)$	$cos(3\; t)\; cos(3x)$

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