Question
Solve the following differential equation:
$\frac{\text{dy}}{\text{dx}}+\text{y}=\text{e}^{-2\text{x}}$
$\frac{\text{dy}}{\text{dx}}+\text{y}=\text{e}^{-2\text{x}}$
Solution of the equation is given by,
$\text{y}\times(\text{I.F.})=\int\text{Q}\times(\text{I.F.})\text{dx + C}$
$\text{y}\times\text{e}^{\text{x}}=\int\text{e}^{-2\text{x}}\times\text{e}^{\text{x}}\text{dx + C}$ $=\int\text{e}^{-\text{x}}+\text{C}$ $\text{y}\text{e}^{\text{x}}=\frac{\text{e}^{-\text{x}}}{-1}+\text{C}$ $\text{y}=-\text{e}^{-2\text{x}}+\text{C}\text{e}^{-\text{x}}$Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.