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

\[f(x)=c_1e^{2x}+c_2+\frac{1}{10}(-15x-8\sin(x)-4\cos(x))\]

Answer 2

how did you get that!!!!!

Answer 3

I solved the ODE you posted.

Answer 4

and how is that equal to 2cosx?

Answer 5

If you take that function and evaluate\[f''-2f'-3f,\]you will get\[2\cos(x).\]

Answer 6

hmm ok