What is the solution for y/x (dy)/(dx)=sqrt((1+x^2)(1+y^2)) ?

The solution for y/x (dy)/(dx)=sqrt((1+x^2)(1+y^2)) is

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y/x (dy)/(dx)=sqrt((1+x^2)(1+y^2))

\frac{y}{x} \frac{d y}{d x} = (1 + x^{2}) (1 + y^{2})

y = \frac{3 x ^{4} + 3 x ^{2} + 6 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} + x ^{6} + 9 c _{1}^{2} - 8}{3}, y = - \frac{3 x ^{4} + 3 x ^{2} + 6 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} + x ^{6} + 9 c _{1}^{2} - 8}{3}

Solution steps

\frac{y}{x} \frac{d y}{d x} = (1 + x^{2}) (1 + y^{2})

Solve separable ODE:

y = \frac{3 x ^{4} + 3 x ^{2} + 6 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} + x ^{6} + 9 c _{1}^{2} - 8}{3}, y = - \frac{3 x ^{4} + 3 x ^{2} + 6 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} + x ^{6} + 9 c _{1}^{2} - 8}{3}

y = \frac{3 x ^{4} + 3 x ^{2} + 6 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} + x ^{6} + 9 c _{1}^{2} - 8}{3}, y = - \frac{3 x ^{4} + 3 x ^{2} + 6 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} + x ^{6} + 9 c _{1}^{2} - 8}{3}

What is the solution for y/x (dy)/(dx)=sqrt((1+x^2)(1+y^2)) ?
The solution for y/x (dy)/(dx)=sqrt((1+x^2)(1+y^2)) is