Question

y'-9y=sen2x+cos2x
method of superposition

Answer 1

Any attempts?

Answer 2

since this is a linear differential equation, if we can find solutions to \(y'-9y=0\), \(y'-9y=\sin(2x)\), and \(y'-9y=\cos(2x)\) in isolation, then the solution to \(y'-9y=\sin(2x)+\cos(2x)\) will be a combination of these

Answer 3

for \(y'-9y=0\) we can separate variables:$$y'=9y\\\frac{y'}y=9\\\int\frac{y'}ydx=\int2\ dx\\\ln|y|=2x+C\\y=Ce^{2x}$$