Suppose that L is a linear operator and f, ..., fk are known functions. Show that...

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Suppose that L is a linear operator and f, ..., fk are known functions. Show that if u,..., u are solutions of the inhomogeneous PDEs L[u] = f1,..., L[u] = fk and c,..., Ck are constants, then u = c1u1+. is a solution of the PDE L[u] = f, where +Ckuk f=c1f1++ Ckfk Suppose that L is a linear operator and f, ..., fk are known functions. Show that if u,..., u are solutions of the inhomogeneous PDEs L[u] = f1,..., L[u] = fk and c,..., Ck are constants, then u = c1u1+. is a solution of the PDE L[u] = f, where +Ckuk f=c1f1++ Ckfk