Answer to Question #124066 in Calculus for Asubonteng Isaac Adjei

Question

Verify that y = e2xsinx is a solution to the differential equation d2y/dx2 - 4dy/dx+5y=0

Answer 1

If $y=e^{2x}\sin x$ then $y'=e^{2x}(2\sin x+\cos x)$ and $y''=2e^{2x}(2\sin x+\cos x)+e^{2x}(2\cos x-sin x)$ hence $y''-4y'+5y=0$