Choose the correct answer from the given four option. Solution of…

MCQ

Choose the correct answer from the given four option.
Solution of differential equation xdy - ydx = 0 represents:

A
A rectangular hyperbola.
B
Parabola whose vertex is at origin.
✓
Straight line passing through origin.
D
A circle whose centre is at origin.

✓

Answer

Correct option: C.

Straight line passing through origin.

Given that, $\text{xdy}-\text{ydx}=0$
$\Rightarrow\text{xdy}=\text{ydx}$

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

On integrating both sides, we get

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

$\Rightarrow\log\text{y}=\log\text{x}+\log\text{C}$

$\Rightarrow\log\text{y}=\log\text{Cx}$

$\Rightarrow\text{y}=\text{Cx}$

Which is a straight line passing through origin.

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