Solve (D^2-1)y=xsinx+x^2e^x

$$( D ^ { 2 } - 1 ) y = x \sin x + x ^ { 2 } e ^ { x }$$

Solve for D (complex solution)

$$\left\{\begin{matrix}D=-iy^{-\frac{1}{2}}\sqrt{-x^{2}e^{x}-x\sin(x)-y}\text{; }D=iy^{-\frac{1}{2}}\sqrt{-x^{2}e^{x}-x\sin(x)-y}\text{, }&y\neq 0\\D\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Solve for D

$$\left\{\begin{matrix}D=\sqrt{\frac{x^{2}e^{x}+x\sin(x)+y}{y}}\text{; }D=-\sqrt{\frac{x^{2}e^{x}+x\sin(x)+y}{y}}\text{, }&\left(y<0\text{ or }-x\left(xe^{x}+\sin(x)\right)\leq 0\text{ or }y\geq -x\left(xe^{x}+\sin(x)\right)\right)\text{ and }\left(y<0\text{ or }x\left(xe^{x}+\sin(x)\right)+y=0\text{ or }y\geq -x\left(xe^{x}+\sin(x)\right)\text{ or }-x\left(xe^{x}+\sin(x)\right)\leq 0\right)\text{ and }\left(y>0\text{ or }-x\left(xe^{x}+\sin(x)\right)\geq 0\text{ or }y\leq -x\left(xe^{x}+\sin(x)\right)\right)\text{ and }y\neq 0\\D\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$