Solve y″ + 2y′ − 8y = 2e^{−2x} − e^{−x} with y(0) = 1, y′(0) = 0 by variation of parameters

Exercise 4.6.21

$Handwritten solution, page 1 of 2. Solve y″ + 2y′ − 8y = 2e^{−2x} − e^{−x} with y(0) = 1, y′(0) = 0 by variation of parameters$ $Handwritten solution, page 2 of 2. Solve y″ + 2y′ − 8y = 2e^{−2x} − e^{−x} with y(0) = 1, y′(0) = 0 by variation of parameters$