Question

Solve the following differential equation:
$\log \left(\frac{dy}{dx}\right)=ax+by$

Answer 1

$\log \left(\frac{dy}{dx}\right)=ax+by$

$\Rightarrow \frac{dy}{dx}=e^{ax+by}=e^{ax}.e^{by}$

$\Rightarrow e^{-by}dy=e^{ax}dx$

Integrate on both sides

$\Rightarrow \frac{e^{-by}}{-by}=\frac{e^{ax}}{ax}+C$, where $C$ is a constant