The general solution of the differential equation $(9x - 3y + 5) dy = (3x - y + 1) dx$ is

The general solution of the differential equation $(3x-4y)(dx-3dy)+(6dx-4dy)=0$ is

If $x \frac{dy}{dx} + y = x \frac{f(xy)}{f'(xy)}$, then $|f(xy)|$ is equal to

Let $S$ be the family of curves given by the general solution of the differential equation $\frac{y^2 e^{-1 / y}}{\sqrt{x}} dx - 2 \sec \sqrt{x} dy = 0$. Then the equation of the curve belonging to $S$ and passing through $(\pi^2, 1)$ is

The solution of the differential equation $\frac{dy}{dx} = \frac{y - x}{y - x - 1}$,given $y(-5) = -5$,represents:

The particular solution of the differential equation $\frac{dy}{dx} = e^{2y} \cos x$,when $y(\frac{\pi}{6}) = 0$ is