$f(x, y) = \frac{1}{x + y}$ is a homogeneous function of degree

One ticket is selected at random from $50$ tickets numbered $00, 01, 02, \ldots, 49$. The probability that the sum of the digits is $10$,given that the product of the digits is $9$,is

The homogeneous differential equation of the form $\left(1+e^{\frac{x}{y}}\right) dx + e^{\frac{x}{y}}\left(1-\frac{x}{y}\right) dy = 0$ can be solved by making the substitution:

The solution of the differential equation $(x^2+y^2) dx - 5xy dy = 0$,$y(1)=0$,is :

If $x^\alpha \frac{dy}{dx} = y^\beta(\gamma \log x + \delta \log y + 1)$ is a homogeneous differential equation,then

The solution of the differential equation $y \sin \left(\frac{x}{y}\right) dx = \left\{x \sin \left(\frac{x}{y}\right) - y\right\} dy$ satisfying $y\left(\frac{\pi}{4}\right) = 1$ is