All that is known concerning a mysterious secondorder consta

All that is known concerning a mysterious second-order constant-coefficient differential equation y^\"+py^\'+qy=g(x) is that x^2+1+e^x cos(x),x^2+1+e^x sin(x), and x^2+1+e^xcos(x)+e^xsin(x) are solutions. Determine two linearly independent solutions to the corresponding homogeneous equation. Find a suitable choice of p, q, and g (x)

Solution