Question

Solution of the differential equation $xdy-ydx=0$ represents a

• A. parabola
• B. circle
• C. hyperbola
• D. straight line

Answer 1

The correct option is D

straight line

Explanation for the correct answer:

Determining the form represented by the given equation.

We have

$$\begin{gathered} xdy-ydx=0 \\ \Rightarrow xdy=ydx \\ \Rightarrow \frac{dy}{y}=\frac{dx}{x} \end{gathered}$$

Integrating the equation on both the sides

$$\begin{gathered} \Rightarrow \log y=\log x+\log C \\ \Rightarrow \log y=\log \left(xC\right)[\because \log (ab)=\log a+\log b] \\ \Rightarrow y=Cx \end{gathered}$$

This solution represents an equation of a straight line $\left(y=mx+c\right)$.

Therefore, the correct answer is option (D).