Differential Equations — Class 12 Maths Solution

Slope of tangent to the curve $= \frac{{dy}}{{dx}}$

and ratio of abscissa to the ordinate $= \frac{x}{y}$

According to the question,

$\frac{{dy}}{{dx}} = \frac{x}{y}$

$ydy = xdx$

On integrating both sides,

we get
$\frac{{{y^2}}}{2} = \frac{{{x^2}}}{2} + C$

$\Rightarrow$ $\frac{{{y^2}}}{2} - \frac{{{x^2}}}{2} = C \Rightarrow {y^2} - {x^2} = 2C$

which is an equation of rectangular hyperbola.