Consider the differential equation:

y'' + 1 y = f(x)

For each choice of the forcing function f(x), indicate the form of the particular solution, without solving for the constants. Example: f(x) = x2 y(x) = A·x2 + B·x + C

f(x) = xe4 x , y(x) = ?

f(x) = cos 5 x , y(x) = ?

f(x) = x sin 3 x , y(x) = ?

f(x) = sin 1 x , y(x) = ?

f(x) = e1 xcos 1 x , y(x) = ?