Are there general methods for solving differential equations involving gradient, for example:
$\frac{dx}{dt}=\frac{dF(x)}{dx}$
Or their systems:
$\frac{dx}{dt}=\frac{dF(x,y)}{dx}$
$\frac{dy}{dt}=\frac{dF(x,y)}{dy}$
where $F(x)$ or $F(x,y)$ - arbitrary function, for example $e^{-(x^2+y^2)}$ or $sech(x)^2 \cdot sech(y)^2$