Solution of differential equation x dy - yx = 0 represents: 1. rectangular hyperbola 2. straight line passing through origin 3. parabola whose vertex is at origin 4. circle whose center is at origin

Solution of differential equation x dy - yx = 0 represents: 1. re…

Question

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

rectangular hyperbola
straight line passing through origin
parabola whose vertex is at origin
circle whose center is at origin

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Answer

straight line passing through origin

Solution:
$=\text{x}\text{ dx}-\text{y}\text{ dx}=0$
$\Rightarrow\frac{\text{dy}}{\text{y}}=\frac{\text{dx}}{\text{x}}$
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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