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).

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you want an exact solution without initial conditions?

or perhaps they just want the particular solution, which you can get with undetermined coefficients

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