Ordinary Differential Equations/Exact 4

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\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}}}} \\ 
 & {{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}{{{e}^{2x}}} \\ 
 & y=\frac{\int{{{x}^{2}}+5{{e}^{2x}}}dx+C}{{{e}^{2x}}}=\frac{\frac{{{x}^{3}}}{3}+\frac{5{{e}^{2x}}}{2}+C}{{{e}^{2x}}} \\ 
 & \underline{y=\frac{{{x}^{3}}}{3{{e}^{2x}}}+\frac{5}{2}+\frac{C}{{{e}^{2x}}}}  
\end{align}