The integrating factor of the differential equation $\frac{dy}{dx} + y \tan x = \sec x$ is . . . . . . .

Let $y=y(x)$ be the solution of the differential equation $\cos x(\ln(\cos x))^2 dy + (\sin x - 3y \sin x \ln(\cos x)) dx = 0$,where $x \in (0, \frac{\pi}{2})$. If $y(\frac{\pi}{4}) = \frac{-1}{\ln 2}$,then $y(\frac{\pi}{6})$ is:

The curve for which the intercept cut off by any tangent on the $y$-axis is proportional to the square of the ordinate of the point of tangency is (where $c_1$ and $c_2$ are arbitrary constants):

The general solution of $x(x-1) \frac{dy}{dx} = x^3(2x-1) + (x-2)y$ is

Which of the following equations is a linear differential equation?

The integrating factor of the differential equation $\cos x \frac{dy}{dx} + y \sin x = 1$ is