Solve second order DEs. Compute the general solution and express it in the form x(t)= xp(t) + xc(t). Show steps such as the characteristic polynomial, the initial guess for xp(t), the (system) of equations needed to determine the unknown coefficiants and the final result
a.) x'' +4x' + 3x = cos (t)
b.) x'' + 5x' +4x= e^(-t)