The solution of the differential equation $log \left(\frac{dy}{dx}\right)=ax+by $ is :

$\frac{1}{b}e^{by}=\frac{1}{a}e^{ax}+C$ Where C is an arbitrary constant $\frac{1}{b}e^{-by}=\frac{1}{a}e^{ax}+C$ Where C is an arbitrary constant $\frac{-1}{b}e^{-by}=\frac{1}{a}e^{ax}+C$ Where C is an arbitrary constant $\frac{-1}{b}e^{by}=\frac{1}{a}e^{ax}+C$ Where C is an arbitrary constant

$\frac{-1}{b}e^{-by}=\frac{1}{a}e^{ax}+C$ Where C is an arbitrary constant