Q. 393.7( 3 Votes )

Solution of differential equation xdy – ydx = 0 represents:
A. a rectangular hyperbola

B. parabola whose vertex is at origin

C. straight line passing through origin

D. a circle whose centre is at origin

Answer :

Let us solve the differential equation

⇒ xdy – ydx = 0

⇒ xdy = ydx

⇒ log y = log x + c

⇒ log y – log x = c

Using log a – log b = log

⇒ y = e^cx

e^c is a constant because e is a constant and c is the integration constant let it be denoted as k hence e^c = k

⇒ y = kx

The equation y = kx is equation of a straight line and (0, 0) satisfies the equation hence

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Solution of differential equation xdy – ydx = 0 represents: A. a rectangular hyperbolaB. parabola whose vertex is at originC. straight line passing through originD. a circle whose centre is at origin