Second Order Nonhomogeneous Differential Equation (Method of Undetermined Coefficients)

Find the general solution of the following Differential equation$y{}^{\u2033}-2{y}^{\prime}+10y={e}^{x}\mathrm{cos}\left(3x\right)$ . We know that the general solution for 2nd order Nonhomogeneous differential equations is the sum of $y}_{p}+{y}_{c$ where $y}_{c$ is the general solution of the homogeneous equation and $y}_{p$ the solution of the nonhomogeneous. Therefore ${y}_{c}={e}^{x}({c}_{1}\mathrm{cos}\left(3x\right)+{c}_{2}\mathrm{cos}\left(3x\right))$ . Now we have to find $y}_{p$ . I know in fact that ${y}_{c}={e}^{x}({c}_{1}\mathrm{cos}\left(3x\right)+{c}_{2}\mathrm{cos}\left(3x\right))$ . Now we have to find yp. I know in fact that $y}_{p}={e}^{\times}\frac{\mathrm{sin}\left(3x\right)}{6$ but i do not know how to get there.

Find the general solution of the following Differential equation