Find y in terms of x given that
d2y/dx2 - 4(dy/dx) + 4y = e^2x
and that dy/dx=1 and y=0 at x=0
I've worked out that the complementary function is (A+Bx)e^2x
However, i don't understand why I should be using y=k(x^2)e^2x as the particular integral and not y=ke^2x
Can anyone explain?