Question

What is the solution of the differential equation $\frac{ydx-xdy}{y^2}=0$?
where $c$ is an arbitrary constant.

• A. $xy=c$
• B. $y=cx$
• C. $x+y=c$
• D. $x-y=c$

Answer 1

Answer: (B)

$y=cx$

$\frac{ydx-xdy}{y^2}=0\Rightarrow ydx=xdy$

$\Rightarrow \frac{dx}{x}=\frac{dy}{y}$

Integrating both the sides, we get

$\int \frac{dx}{x}=\int \frac{dy}{y}$

$\Rightarrow \ln \left(cx\right)=\ln \left(y\right)\Rightarrow y=cx$

where $c$ is an arbitrary constant.