Variation of parameters: Difference between revisions

Revision as of 21:12, 3 June 2022

Revision as of 14:06, 22 August 2022

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: <math>\lambda^2+4\lambda+4=(\lambda+2)^2=0 </math>

Since <math>\lambda=-2</math> is a repeated root, we have to introduce a factor of ''x'' for one solution to ensure linear independence: ''u''<submath>1</sub>&nbsp; u_1 =&nbsp;'' e''<sup>−2''x''^{-2x} </supmath> and ''u''<submath>2</sub>&nbsp; u_2 =&nbsp;''xe''<sup>−2''x'' e^{-2x}</supmath>. The [[Wronskian]] of these two functions is

: <math>W=\begin{vmatrix}