alleryStart learning →The general solution of $\dfrac{dy}{dx} + y = e^{-x}$ is:
- $y \cdot e^x = x + c$
- $y = e^{-x}(x + c)$
- Both A and B are equivalent
- $y = x e^x + c$
Show answer and solution
Correct answer: C. Both A and B are equivalent
Linear DE with $P = 1, Q = e^{-x}$. IF = $e^x$.
$y \cdot e^x = \int e^{-x}\cdot e^x dx + c = x + c$.
**So $y \cdot e^x = x + c$, equivalent to $y = e^{-x}(x + c)$.**