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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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