Question
The 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 ✓ Correct
- (d) a circle whose centre is at origin
Differential Equations — Class 12 Maths Solution
Step-by-step Solution
Given that, $xdy - ydx = 0$
$\Rightarrow$ $xdy = ydx$
$\Rightarrow$ $\frac{{dy}}{y} = \frac{{dx}}{x}$
On integrating both sides,
we get
$\log y = \log x + \log C$
$\Rightarrow$ $\log y = \log Cx$
$\Rightarrow$ $y = Cx$
which is a straight line passing through origin.
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Differential Equations. Curated by Sachin Sharma. Free for all students.