Answer
$\frac{y^{2}}{2}$ = $\frac{x^{2}}{2}$ + 2
(OR)
$y^{2}$ - $x^{2}$ = $4$
Work Step by Step
m = $\frac{dy}{dx}$ = $\frac{x}{y}$
$\int ydy$ = $\int xdx$
$\frac{y^{2}}{2}$ = $\frac{x^{2}}{2}$ + c
If the curve passes through (0, 2), then at x=0; y=2.
Hence, $\frac{4}{2}$ = 0 + c
Thus, c = 2.
Hence, $\frac{y^{2}}{2}$ = $\frac{x^{2}}{2}$ + 2
(OR)
$y^{2}$ - $x^{2}$ = $4$
