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

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

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

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

y = 2 arcsin (x) + c_{1}, y = - 2 arcsin (x) + c_{1}

Solution steps

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

Solve separable ODE:

y = 2 arcsin (x) + c_{1}, y = - 2 arcsin (x) + c_{1}

y = 2 arcsin (x) + c_{1}, y = - 2 arcsin (x) + c_{1}

2 x y + (1 + x^{2}) \cdot y^{^{'}} = 0

y^{^{'}} = 8 t cos^{2} (y), y (1) = \frac{3 π}{4}

\frac{d}{d x} (\frac{x ^{8}}{y ^{5}}) = 0

y^{^{'}} = (\frac{1}{1 + x}) y

y = \frac{3 ( 1 + 3 x ^{2} ) ^{2}}{x} \frac{d y}{d x}

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