Differential Equations Question 131
Question: The differential equation of all straight lines passing through the origin is
[DCE 2002; Kerala (Engg.) 2002; UPSEAT 2004]
Options:
A) $ y=\sqrt{x\frac{dy}{dx}} $
B) $ \frac{dy}{dx}=y+x $
C) $ \frac{dy}{dx}=\frac{y}{x} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
The equation of all straight lines passing through the origin is $ y=mx $
……..(i) where m is arbitrary constant Differentiate (i) w.r.t. x, we get $ \frac{dy}{dx}=m $
Therefore $ \frac{dy}{dx}=\frac{y}{x} $ , (By (i)).
BETA
