Second Order Linear Differential Equations
The first thing we need to know is that an initial-value problem has a solution, and that it is unique. THEOREM 1. (Existence and Uniqueness Theorem) Given the second order linear equation (1). Let a be any point on the interval I, and let α and β be any two real numbers. Then the initial-value problem y00 +p(x)y0 +q(x)y= f(x),y(a)=α, y0(a)=β
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