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4.43 Principle of linear superposition

Proposition

Let $y_{1}$ and $y_{2}$ be solutions of the homogeneous linear differential equation

a{{d^{2}y}\over{dx^{2}}}+b{{dy}\over{dx}}+cy=0.

∗

Then

y=Ay_{1}+By_{2}

is also a solution for all constants $A$ and $B$ .

This follows easily from 3.6(i) and (ii).