Ordinary Differential Equations/Exact 4

$$\begin{align} & \text{Q1 answer:} \\ & \frac{dy}{dx}+2y={{x}^{2}}{{e}^{-2x}}+5 \\ & y=\frac{\int{{{e}^{\int{P\left( x \right)dx}}}Q\left( x \right)dx}+C} \\ & {{e}^{\int{P\left( x \right)dx}}} \\ & P\left( x \right)=2 \\ & {{e}^{\int{2dx}}}={{e}^{2x}} \\ & Q\left( x \right)={{x}^{2}}{{e}^{-2x}}+5 \\ & y=\frac{\int{\left( {{e}^{2x}} \right)\left( {{x}^{2}}{{e}^{-2x}}+5 \right)}dx+C} \\ & y=\frac{\int{{{x}^{2}}+5{{e}^{2x}}}dx+C}=\frac{\frac{3}+\frac{5{{e}^{2x}}}{2}+C} \\ & \underline{y=\frac{3{{e}^{2x}}}+\frac{5}{2}+\frac{C}} \end{align}$$