The general solution of ${x^2}\frac{{dy}}{{dx}} = 2$ is

The solution of the differential equation $(1 + x^2)\frac{dy}{dx} = x(1 + y^2)$ is

The general solution of the differential equation $(3x-4y)(dx-3dy)+(6dx-4dy)=0$ is

The general solution of the differential equation $\frac{dy}{dx} = \cos^2(3x+y)$ is $\tan^{-1}\left(\frac{\sqrt{3}}{2} \tan(3x+y)\right) = f(x)$. Then,$f(x) =$

The solution of the differential equation $y \, dx - x \, dy + x y^2 \, dx = 0$ is:

Find the equation of the curve passing through the point $\left(0, \frac{\pi}{4}\right)$ whose differential equation is $\sin x \cos y \, dx + \cos x \sin y \, dy = 0$.