$\sin x-\log \left(1+x^2\right)=\log y+c$

$(\log y)^2+2 \cos x+\log \left(1+x^2\right)^2=c$

$\log y=2 \cos x+\log \left(1+x^2\right)+c$

$\frac{\log y}{y}=2 \sin x+\cos x \log \left(1+x^2\right)+c$

$x y^{\prime \prime}+x\left(y^{\prime}\right)^2-y y^{\prime}=0$

$x y y^{\prime \prime}+x\left(y^{\prime}\right)^2-y=y^{\prime}$

$y^{\prime \prime}+\frac{\left(y^{\prime}\right)^2}{y}-\frac{y}{x}=0$

$y^{\prime \prime}+\left(y^{\prime}\right)^2+x^2 y^2=0$

4

3

6

Not defined

$x-3 y+\frac{22}{3} \log |3 x-7|+c=0$

$x-3 y+\frac{8}{3} \log |6 x-9 y-1|+c=0$

$3 x-3 y+\frac{8}{3} \log |3 x-9 y+1|+c=0$

$3 x-2 y+\frac{22}{3} \log |2 x-3 y-7|+c=0$