Question 1:Consider the following equation:dydx+2y=x2e−2x+5{\displaystyle {\begin{aligned}&{\text{Question 1:}}\\&{\text{Consider the following equation}}:\\&{\frac {dy}{dx}}+2y={{x}^{2}}{{e}^{-2x}}+5\\\end{aligned}}}
find the general solution of the above equation{\displaystyle {\text{find the general solution of the above equation}}}
hint: using the following: y=∫e∫P(x)dxQ(x)dx+Ce∫P(x)dx{\displaystyle y={\frac {\int {{{e}^{\int {P\left(x\right)dx}}}Q\left(x\right)dx}+C}{{e}^{\int {P\left(x\right)dx}}}}}