Question

Solve the differential equation. (Check my work :D )

Answer 1

\[y' + 2y = 5\sin(e^{2x})\]

Answer 2

\[e \int\limits_{}^{}1^{2dx}=e^{2x}\]\[e^{2x}*dy/dx + e^{2x}*2y = e^{2x} * 5\sin(e^{2x})\]\[\frac{ d(e^{2x}*2y }{ dx }=e^{2x}*5\sin(e^{2x})\]\[\int\limits_{}^{}d(2y * e^{2x}) = 5\int\limits_{}^{}e^{2x}*\sin(e^{2x})dx\]\[u = e^{2x}, du = (1/2)e^{2x}dx\]\[2y*e^{2x}=5\int\limits_{}^{}sinu(2du)\]\[2y*e^{2x}=-10cosu+C\]\[2y*e^{2x}=-10\cos(e^{2x})+C = > y = \frac{ -10\cos(e^{2x})+C }{ 2e^{2x} }\]

Answer 3

The answer is wrong, where did I "goof'ed" up at?

Answer 4

I don't understand your integrating factor.. why is there a 1 to some power?

Answer 5

Having trouble formatting the LaTeX or something?