Principle of superposition

Definition

Suppose that $f_1,\dots f_n$ are solutions of first order linear equation $y^{\prime }+p(t)y=q(t)$. Then any affine linear combination of these functions is also a solution.

If furthermore $q(t)=0$, then any linear combination of these functions is a solution to the equation.

This theorem says that combination of solutions are again solutions, and is called principle of superposition.