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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d P}{d t} = 2 Pt, P (1) = 5

\frac{d P}{d t} = 2 Pt, P (1) = 6

\frac{d P}{d t} = 2 Pt, P (1) = 3

\frac{d y}{d x} = (1 + 2 x) y, y (0) = 1

3 y^{^{'}} + 2 y = 0

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