Question

we have y''-4y=2 and y₁(x)=e⁻²ˣ is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution y₂(x) of the homogeneous equation and a particular solution of the given non-homogeneous equation

Answer 1

\[y_2=y_1\int \frac{e^{-\int P(x)}}{(y_1)^2}\]

Answer 2

or the long way is simply:

y2 = u*y