What is the solution for sqrt(1-y^2)(dx)-sqrt(1+x^2)(dy)=0 ?

The solution for sqrt(1-y^2)(dx)-sqrt(1+x^2)(dy)=0 is y=sin(ln(sqrt(x^2+1)+x)+c_{1})

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sqrt(1-y^2)(dx)-sqrt(1+x^2)(dy)=0

1 - y^{2} (d x) - 1 + x^{2} (d y) = 0

y = sin (ln (x^{2} + 1 + x) + c_{1})

Solution steps

1 - y^{2} (d x) - 1 + x^{2} (d y) = 0

Solve separable ODE:

y = sin (ln (x^{2} + 1 + x) + c_{1})

y = sin (ln (x^{2} + 1 + x) + c_{1})

What is the solution for sqrt(1-y^2)(dx)-sqrt(1+x^2)(dy)=0 ?
The solution for sqrt(1-y^2)(dx)-sqrt(1+x^2)(dy)=0 is y=sin(ln(sqrt(x^2+1)+x)+c_{1})