Question 1: Consider the following equation : d y d x + 2 y = x 2 e − 2 x + 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 ) d x Q ( x ) d x + C e ∫ P ( x ) d x {\displaystyle y={\frac {\int {{{e}^{\int {P\left(x\right)dx}}}Q\left(x\right)dx}+C}{{e}^{\int {P\left(x\right)dx}}}}}