The equation of the curve at every point of which the tangent line has a slope of 2x

Slope of tangent line
$\Rightarrow \frac{dy}{dx}=2x$
dy =2x dx 
Integrating both the sides, we get 
$\int dy=\int 2xdx$
$\begin{array}{r}y=2\times \frac{x^2}{2}+c\\ \therefore y=x^2+c.\end{array}$
this is the required equation of curve