ordinary differential equations – finding a particular solution for inhomogeneous DE: $ y & # 39; & # 39; – y + + frac {1} {4} y = 3 + e ^ frac {x} {2} $

I have the inhomogeneous differential equation:

$ y & # 39; & # 39; – y + + frac {1} {4} y = 3 + e ^ frac {x} {2} $

I start by finding the specific solution, and here I am stuck. At first I know that I have to $ y_p = y_ {p1} + y_ {p2} $

From where $ y_ {p1} $ will be in shape $ Ax ^ 2 + Bx + C $ and $ y_ {p2} $ will be in shape $ De ^ { frac {x} {2}} $

$ y_ {p2} $$ & # 39; = frac {1} {2} De ^ { frac {x} {2}} $

$ y_ {p2} $$ & # 39; & # 39; = frac {1} {4} De ^ { frac {x} {2}} $

Connect this to the above differential equation and look for it $ e ^ { frac {x} {2}} $ on the right side I get:

$ frac {1} {4} D – frac {1} {2} D + frac {1} {4} D = 1 $

$ 0D = 1 $?

Where do I go from here?