Second Order Linear Differential Equations
sition, let y erx so that y rerx y r2erx. Substituting into equation (12.10): (12.11) r2erx are rx berx erx r2 ar b 0 if and only if r is a root of the auxiliary equation. 12.1 Homogeneous Equations 177 Now unfortunately a quadratic equation does not necessarily always have …
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