Homogeneous Function

Q. If $x\frac{dy}{dx}=y(logy-logx+1)$, then the solution of the equation is

1. $ylog\left(\frac{x}{y}\right)=cx$
2. $xlog\left(\frac{y}{x}\right)=cy$
3. $log\left(\frac{y}{x}\right)=cx$
4. $log\left(\frac{x}{y}\right)=cx$

Q. The degree of the homogeneous function $x^2\sin \left(\frac{y^2}{x^2}\right)+y^2$is ___

Q. Solution of the equation $xdy=(y+x\frac{f\left(\frac{y}{x}\right)}{f^{\prime }\left(\frac{y}{x}\right)})dx$

1. $f\left(\frac{x}{y}\right)=cy$
2. $f\left(\frac{y}{x}\right)=cx$
3. $f\left(\frac{y}{x}\right)=cxy$
4. $f\left(\frac{y}{x}\right)=0$