The integrating factor of $\frac{dy}{dx} + \frac{y}{x} = x^3 - 3$ is

Find the equation of a curve passing through the point $(0,1)$. If the slope of the tangent to the curve at any point $(x, y)$ is equal to the sum of the $x$ coordinate (abscissa) and the product of the $x$ coordinate and $y$ coordinate (ordinate) of that point.

The graph of the function $y = f(x)$ passing through the point $(0, 1)$ and satisfying the differential equation $\frac{dy}{dx} + y \cos x = \cos x$ is such that

If $x \, dy = y(dx + y \, dy)$,$y(1) = 1$,$y(x) > 0$,then $y(-3)$ is

If $x dy + (y + y^2 x) dx = 0$ and $y = 1$ at $x = 1$,then

If the slope of the tangent drawn at any point $(x, y)$ on a curve is $(x+y)$,then the equation of that curve is