The integrating factor of $x \frac{dy}{dx} - 2y = x^2 + \sin \left( \frac{1}{x^2} \right)$ is

The integrating factor of the differential equation $(1 - x^2) \frac{dy}{dx} - xy = 1$ is

Let the solution curve $y = y(x)$ of the differential equation $\frac{dy}{dx} - \frac{3x^5 \tan^{-1}(x^3)}{(1+x^6)^{3/2}} y = 2x \exp \left( \frac{x^3 - \tan^{-1}(x^3)}{\sqrt{1+x^6}} \right)$ pass through the origin. Then $y(1)$ is equal to:

The general solution of the differential equation $x^{2} dy - 2xy dx = x^{4} \cos x dx$ is

The integrating factor of the differential equation $\sin y \left(\frac{d y}{d x}\right) = \cos y (1 - x \cos y)$ is

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