Solution of differential equation x dy - yx = 0 represents: - Vidyadip

MCQ

Solution of differential equation x dy - yx = 0 represents:

A
rectangular hyperbola
✓
straight line passing through origin
C
parabola whose vertex is at origin
D
circle whose center is at origin

✓

Answer

Correct option: B.

straight line passing through origin

$=\text{x}\text{ dx}-\text{y}\text{ dx}=0$

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

Integrating both sides

y = ln x ⇒ y = x

Solution of differential equation

x dy - y x = 0

reperesnts straight line passing through origin

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