Solution of differential equation xdy – ydx = 0 represents

  1. a rectangular hyperbola
  2. straight line passing through origin
  3. parabola whose vertex is at origin
  4. circle whose centre is at origin


In the question we have to find the solution of the given equation by integrating it then we will observe the equation and determine the characteristic.

The correct answer is: straight line passing through origin

    Given, x dy – y dx = 0
    rightwards double arrow x. d y equals y. d x
rightwards double arrow 1 over y. fraction numerator d y over denominator d x end fraction equals 1 over x. fraction numerator d x over denominator d y end fraction
i n t e g r a t i n g space b o t h space s i d e s space w e space g e t
rightwards double arrow log space y equals log x
rightwards double arrow y equals x
S o comma space t h e space e q u a t i o n space r e p r e s e n t s space a space s t r a i g h t space l i n e space p a s sin g space t h r o u g h space t h e space o r i g i n.

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