<s>[INST] Find this ODE solution $(y-x)\sqrt{x^2+1}\dfrac{dy}{dx}=(1+y^2)^{\frac{3}{2}}$ Find all solutions $y$ to the ODE
$$(y-x)\sqrt{x^2+1}\dfrac{dy}{dx}=(1+y^2)^{\frac{3}{2}}$$
My try:
$$(y-x)\dfrac{d(\sqrt{1+y^2})}{y}=\dfrac{(1+y^2)dx}{\sqrt{x^2+1}}$$
then
$$\dfrac{(y-x)\cdot d(\sqrt{1+y^2})}{y(1+y^2)}=\dfrac{d(\sqrt{1+x^2})}{x}$$
then I can't.Thank you for you help 
 [/INST] Another CAS gave this "nice" expression 
$$x(y)=\frac{-2 c_1 y+2 c_1 \tan ^{-1}(y)-c_1^2-\tan ^{-1}(y)^2+2 y \tan ^{-1}(y)+1}{c_1^2
   y-2 c_1 y \tan ^{-1}(y)-2 c_1-y+y \tan ^{-1}(y)^2+2 \tan ^{-1}(y)}$$ which simplifies if $y(0)=0$ but does not change to be more pleasant.
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