Question

The differential equation of the family of lines passing through the origin is

• A. $x\frac{dy}{dx} + y = 0$
• B. $x\frac{dy}{dx} = 0$
• C. $x\frac{dy}{dx} - y = 0$
• D. $\frac{dy}{dx} = x$

Hint:

Lines through origin have slope $m = y/x$, giving $x dy = y dx$.

Answer 1

The Correct Option is C

Step 1: Line through origin: $y = mx$.}
Step 2: $\frac{dy}{dx} = m = \frac{y}{x} \Rightarrow x\frac{dy}{dx} - y = 0$.}
Step 3: Final Answer: $x\frac{dy}{dx} - y = 0$.}