Solution of differential equation xdy - ydx = 0 represents:

Question

Solution of differential equation xdy - ydx = 0 represents: (A) rectangular hyperbola. (B) parabola whose vertex is at origin. (C) circle whose centre is at origin. (D) straight line passing through origin.

Tardigrade Admin · Accepted Answer

Given: xdy - ydx = 0
Dividing by xy on both sides,
we get:

\frac{d y}{y} - \frac{d x}{x} = 0

\Rightarrow \frac{d y}{y} = \frac{d x}{x}

By integrating on both sides, we get, log y = log x + log c

\Rightarrow lo g \frac{y}{x} = lo g c

\Rightarrow y = c x

or

y - c x = 0

which represents a straight line passing through origin.

Q. Solution of differential equation xdy - ydx = 0 represents:

rectangular hyperbola.

parabola whose vertex is at origin.

circle whose centre is at origin.

straight line passing through origin.

Given: xdy - ydx = 0 Dividing by xy on both sides, we get: ydy​−xdx​=0 ⇒ydy​=xdx​ By integrating on both sides, we get, log y = log x + log c ⇒logxy​=logc ⇒y=cx or y−cx=0 which represents a straight line passing through origin.