What is the solution for (dy)/(dx)=10xsqrt(25-y^2) ?

The solution for (dy)/(dx)=10xsqrt(25-y^2) is y=5sin(5x^2+c_{1})

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(dy)/(dx)=10xsqrt(25-y^2)

\frac{d y}{d x} = 10 x 25 - y^{2}

y = 5 sin (5 x^{2} + c_{1})

Solution steps

\frac{d y}{d x} = 10 x 25 - y^{2}

Solve separable ODE:

y = 5 sin (5 x^{2} + c_{1})

y = 5 sin (5 x^{2} + c_{1})

y^{^{'}} = \frac{13 x}{y + x ^{2} y}

x^{^{'}} = x + x a^{2}

x 1 + y^{2} + x y^{^{'}} 1 + x^{2} = 0

\frac{d y}{d x} = 5 x^{2} y^{3}

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

What is the solution for (dy)/(dx)=10xsqrt(25-y^2) ?
The solution for (dy)/(dx)=10xsqrt(25-y^2) is y=5sin(5x^2+c_{1})