Question

Let T : C∞(R) −→ C∞(R) be the map given by
T(f) = f′′− 2f′− 3f .

Find a linear combination a sin(x) + b cos(x) which solves the equation
f′′− 2f′− 3f = 2 cos(x).

Answer 1

differentiate your linear combination a couple times ...plug into differential equation ...solve for a,b