If $x d y+\left(y+y^2 x\right) d x=0$ and $y=1$ at $x=1$, then

The solution of $x d y-y d x=\sqrt{x^2+y^2} d x$ when $y(\sqrt{3})=1$ is

The differential equation representing the family of circles having their centres of Y -axis is $\left(y_1=\frac{d y}{d x}\right.$ and $\left.y_2=\frac{d^2 y}{d x^2}\right)$

The general solution of the differential equation $\left(\sin y \cos ^2 y-x \sec ^2 y\right) d y=(\tan y) d r$, is