8.1.2.113 Second Order Differential Equations

Condition: Find a private solution to the differential equation: \ [\ begin {array} {l} y^{\ prime \ prime} -4 y^{\ prime} +3 y = e^{3 x} \\ y (0) = 3, \ quadad y^{\ prime} (0) = 9 \ end {array} \]