Question Number 169342 by Mastermind last updated on 29/Apr/22
$${Obtain}\:{the}\:{differential}\:{equation} \\ $$$${associated}\:{with}\:{the}\:{primitive} \\ $$$${y}\:=\:{Ae}^{\mathrm{2}{x}} +{Be}^{{x}} +{C} \\ $$$$ \\ $$$${Mastermind} \\ $$
Answered by cortano1 last updated on 29/Apr/22
$${y}\:'=\mathrm{2}{Ae}^{\mathrm{2}{x}} +{Be}^{{x}} \\ $$$${y}''=\mathrm{4}{Ae}^{\mathrm{2}{x}} +{Be}^{{x}} \\ $$$$\:\mathrm{2}{y}'=\mathrm{4}{Ae}^{\mathrm{2}{x}} +\mathrm{2}{Be}^{{x}} \\ $$$$\:\:{y}''=\mathrm{4}{Ae}^{\mathrm{2}{x}} +{Be}^{{x}} \\ $$$$\Rightarrow\mathrm{2}{y}'−{y}''=\:{Be}^{{x}} \\ $$