Variation of Parameters (Particular Integral)

For $$\frac{d^2y}{dx^2} + a\frac{dy}{dx} + by = R(x)$$ with known $$y_c = C_1 y_1 + C_2 y_2$$.
Assume $$y_p = u y_1 + v y_2$$.
Solve: $$u' y_1 + v' y_2 = 0$$ and $$u' y_1' + v' y_2' = R(x)$$.
Find $$u = \int \frac{-y_2 R}{W} dx$$, $$v = \int \frac{y_1 R}{W} dx$$, where $$W = y_1 y_2' - y_2 y_1'$$.