The general solution of the differential equation $\log \left(\frac{d y}{a x}\right)=a x+b y$ is

Question

Aicharya · Accepted Answer

Given differential equation $\begin{array}{llll} & \log \left(\frac{d y}{d x}\right) =a x+b y \ \Rightarrow & \frac{d y}{d x}=e^{a x+b y} =e^{a x} \cdot e^{b y} \ \Rightarrow & \int e^{-b y} d y =\int e^{a x} d x \Rightarrow-\frac{1}{b} e^{-b y}=\frac{1}{a} e^{a x}+c^1 \ \Rightarrow & b e^{a x}+a e^{-b y} =c \end{array}$ Hence, option (a) is correct.

The general solution of the differential equation \(\log \left(\frac{d y}{a x}\right)=a x+b y\) is

Solution