What is the solution for (dy)/(dx)=4xsqrt(1-y^2) ?

The solution for (dy)/(dx)=4xsqrt(1-y^2) is y=sin(2x^2+c_{1})

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(dy)/(dx)=4xsqrt(1-y^2)

\frac{d y}{d x} = 4 x 1 - y^{2}

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

Solution steps

\frac{d y}{d x} = 4 x 1 - y^{2}

Solve separable ODE:

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

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

\int (1 - cos (x)) d x

\int \frac{1}{e ^{2 x} + 1} d x

\int (4 - x) x d x

y^{^{'}} + 3 y = t + e^{(- 2 t)}

x \to - 3 lim (\frac{1}{( x + 3 ) ^{2}})

What is the solution for (dy)/(dx)=4xsqrt(1-y^2) ?
The solution for (dy)/(dx)=4xsqrt(1-y^2) is y=sin(2x^2+c_{1})