Differential Equations with Repeated Roots: Explained in 3 Ways

We explore 3 different explanations why the solution is of the form (A + Bx) e^{lambda x}, for a 2nd order linear homogeneous differential equation whose auxiliary equation has repeated root lambda. 00:00 Intro 00:38 Background: Distinct roots case 06:59 Explanation 1: Reduction of order derivation 10:36 Explanation 2: Variation of parameters 15:39 Explanation 3: Taking limits