Question: Find and use the initial value Green's function to solve [x^{2} y^{prime prime}+3 x y^{prime}-15 y=x^{4} e^{x}, y(1)=1, y^{prime}(1)=0]

Find and use the initial value Green's function to solve

\[x^{2} y^{\prime \prime}+3 x y^{\prime}-15 y=x^{4} e^{x}, y(1)=1, y^{\prime}(1)=0\]

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