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प्रश्न
Solution of differential equation xdy – ydx = 0 represents : ______.
विकल्प
A rectangular hyperbola
Parabola whose vertex is at origin
Straight line passing through origin
A circle whose centre is at origin
उत्तर
Solution of differential equation xdy – ydx = 0 represents : straight line passing through origin.
Explanation:
The given differential equation is xdy – ydx = 0
⇒ `("d"y)/("d"x) = y/x`
⇒ `("d"y)/y = ("d"x)/x`
Integrating both sides, we get
`int ("d"y)/y = ("d"x)/x`
⇒ log y = log x + log c
⇒ log y = log xc
⇒ y = xc
Which is a straight line passing through the origin.
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