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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d}{d y} (y^{2} + y)

\int \frac{3 x}{1 - 9 x ^{4}} d x

\int \frac{\frac{1}{120}}{- P + 120} d P

tan (sin (x))

\frac{d y}{d x} = \frac{( e ^{x} - e ^{- x} )}{( 3 + 4 y )}

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