Integrating factor of $(x+2 y^3) \frac{d y}{d x}=y^2$ is

The integrating factor of the differential equation $(1 + t^2) + (x - e^{\tan^{-1} t}) \frac{dt}{dx} = 0$ is

Find the general solution of the differential equation $y dx - (x + 2y^2) dy = 0$.

The general solution of the differential equation $\frac{dy}{dx} + (\sec x \operatorname{cosec} x) y = \cos^2 x$ is

The equation of the curve passing through the point $(0,2)$ given that the sum of the ordinate and abscissa of any point exceeds the slope of the tangent to the curve at that point by $5$ is

Let $y=y(x)$ be the solution of the differential equation $x(1-x^{2}) \frac{dy}{dx}+(3x^{2}y-y-4x^{3})=0, x>1$ with $y(2)=-2$. Then $y(3)$ is equal to