The equation of the curve whose slope at any point is equal to $2 x y$ and which passes through the point…
The equation of the curve whose slope at any point is equal to $2 x y$ and which passes through the point $(0,1)$ is
$\log y=x^{2}$
$\log y=\frac{1}{x}$
$\frac{1}{y}=x$
$\log y=x$
Solution
We have $\frac{d y}{d x}=2 x y$
$\therefore \int \frac{\mathrm{dy}}{\mathrm{y}}=\int 2 \mathrm{x} \mathrm{dx}$
$\Rightarrow \log y=\frac{2 x^{2}}{2}+C$
$\log y=x^{2}+C$ and curve passes through point $(0,1)$.
At $x=0, y=1$, we get $C=0$
$\therefore \log y=x^{2}$