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

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

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

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

y = sin (arcsin (x) + \frac{1}{2} sin (2 arcsin (x)) + c_{1})

Solution steps

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

Solve separable ODE:

y = sin (arcsin (x) + \frac{1}{2} sin (2 arcsin (x)) + c_{1})

y = sin (arcsin (x) + \frac{1}{2} sin (2 arcsin (x)) + c_{1})

3 \frac{d y}{d x} = \frac{4 x}{y ^{2}}

y^{^{'}} = 4 x + x y, y (0) = - 2

y^{^{'}} = 4 x + x y, y (0) = - 1

\frac{d y}{d x} y = 5 x^{3}

\frac{d y}{d x} 2 x + y = 0

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