Solution of the differential equation \(

CUET Preparation Today

Start Free Mocks

Home Questions ZVUU5667NE

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

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

Options:

$be^{ax}+ae^{-by}+c=0$

$\frac{e^{ax}}{a}-\frac{e^{-by}}{b}+c=0$

$e^{ax}+e^{-by}+c=0$

$e^{ax+by}=c(ax+by)$

Correct Answer:

$be^{ax}+ae^{-by}+c=0$

Explanation:

$\frac{dy}{dx}=e^{ax}e^{ay}⇒\int e^{-by}dy=\int e^{ax}dx$

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

so $be^{ax}+ae^{-by}=c'$