Question

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

• A. $\frac{e^{-by}}{b}+\frac{e^{ax}}{a}+c=0$
• B. $\frac{e^{ax}}{b}-\frac{e^{-by}}{a}=c$
• C. $\frac{e^{ax}}{b}+\frac{e^{-by}}{a}=c$
• D. $Noneofthese$

Answer 1

The correct option is A $\frac{e^{-by}}{b}+\frac{e^{ax}}{a}+c=0$

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

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

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

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

Integrating both sides, we get

$\frac{-e^{-by}}{b}=\frac{e^{ax}}{a}+c$