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•• Consider the second-order differential equation
f(x)ψ″ (x) + b(x)ψ′(x) + h(x)ψ(x) = 0
where f, g, and h are known functions of x. Prove that if ψ1 (x) and ψ2 (x) are both solutions of this equation, the linear combination Aψ1(x)+ Bψ2(x) is also a solution for any two constants A and B — the result known as the superposition principle.
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