Question: Determine (by substitution) that the given function is a solution of the given PDEs. (Hint: read textbook EK page 541 for common type of equations)

Determine (by substitution) that the given function is a solution of the given PDEs. (Hint: read textbook EK page 541 for common type of equations) (1) Determine whether : u(x,t)=sin(kct)cos(kx) is a solution of the 1D wave (string vibration) equation. (2) Determine whether: u(x,t)=etsin(x) is a solution of the 1D heat equation. (3) Determine whether: u(x,t)=excos(y) is a solution of the 2D Laplace equation

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