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})

\frac{d}{d x} (500 (1 + \frac{4 x}{50 + x ^{2}}))

\int z^{'} d z

\int \frac{x ^{2}}{x ^{2} - 49} d x

(2 x + 3) + (2 y - 2) \frac{d y}{d x} = 0

3 x^{2} + 2 x y + 3 y^{2} + (x^{2} + 6 x y) y^{^{'}} = 0

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})