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

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

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(dx)/(dy)=xsqrt(1-y^2)

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

x = e^{\frac{1}{2} (a r c s i n (y) + \frac{1}{2} s i n (2 a r c s i n (y))) + c_{1}}

Solution steps

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

Solve separable ODE:

x = e^{\frac{1}{2} (a r c s i n (y) + \frac{1}{2} s i n (2 a r c s i n (y))) + c_{1}}

x = e^{\frac{1}{2} (a r c s i n (y) + \frac{1}{2} s i n (2 a r c s i n (y))) + c_{1}}

\frac{x}{3}

y^{^{''}} - 7 y^{^{'}} + 10 y = e^{3 x}

\frac{\partial}{\partial x} (2 \cdot z \cdot cos (x))

x \to 0 lim (\frac{2 ln ( x + 1 )}{x})

3 e^{- x^{2}}

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