Math Problem Solver

solve the problem operator D problem \( \frac{d^{2} y}{d x^{2}}-y=12 x^{2} e^{x} \) sum following the same steps shown i the following sum \[\begin{array}{l}2 \frac{d^{3}}{3 x^{2}}-7 \frac{d y}{3 x}-4 y=e^{3 x} \\\frac{C F}{A \cdot E}\left(2 m^{2}-7 m-4=0\right) \\(m-8)(m+1)=0 \\m=8 \quad m=-1 \quad y=A e^{8 x}+R e^{-x}\end{array}\] \[\begin{array}{l}\left(2 D_{y}^{2}-7\right) y-4 y=e^{3 x} \\y=\frac{1}{2 D^{2}-7 D-4}\left\{e^{3 x}\right\} \\y=e^{3 x} \frac{1}{2(3)^{2}-7(3)-4} \\y=e^{3 x}-\frac{1}{18-21-4} \\y=e^{3 x} \frac{1}{7} \\y=-\frac{e^{3 x}}{7}\end{array}\] \( y=A e^{8 x}+B e^{-x}+e^{3 x}-\frac{1}{7} \)