What is the solution for (dy)/(dx)=8xsqrt(9-y^2) ?

The solution for (dy)/(dx)=8xsqrt(9-y^2) is y=3sin(4x^2+c_{1})

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(dy)/(dx)=8xsqrt(9-y^2)

\frac{d y}{d x} = 8 x 9 - y^{2}

y = 3 sin (4 x^{2} + c_{1})

Solution steps

\frac{d y}{d x} = 8 x 9 - y^{2}

Solve separable ODE:

y = 3 sin (4 x^{2} + c_{1})

y = 3 sin (4 x^{2} + c_{1})

e^{x^{2}} \frac{d y}{d x} - x y = 0

y^{^{'}} = \frac{x ^{2} - 2}{y}

y^{^{'}} + \frac{y ^{^{'}}}{x} + (1 - \frac{1}{4 x ^{2}}) y = 0

y y^{^{'}} - sin (x) = 0, y (π) = 1

csc (y) d y + sec^{2} (x) d x = 0

What is the solution for (dy)/(dx)=8xsqrt(9-y^2) ?
The solution for (dy)/(dx)=8xsqrt(9-y^2) is y=3sin(4x^2+c_{1})