What is the solution for (dy)/(dx)=(y^2)/(sqrt(-x^2+100)) ?

The solution for (dy)/(dx)=(y^2)/(sqrt(-x^2+100)) is y=-1/(arcsin(1/10 x)+c_{1)}

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(dy)/(dx)=(y^2)/(sqrt(-x^2+100))

\frac{d y}{d x} = \frac{y ^{2}}{- x ^{2} + 100}

y = - \frac{1}{arcsin ( \frac{1}{10} x ) + c _{1}}

Solution steps

\frac{d y}{d x} = \frac{y ^{2}}{- x ^{2} + 100}

Solve separable ODE:

y = - \frac{1}{arcsin ( \frac{1}{10} x ) + c _{1}}

y = - \frac{1}{arcsin ( \frac{1}{10} x ) + c _{1}}

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

y^{^{'}} = x^{2} cos (y) + x^{2} + 1 + cos (y)

\frac{d y}{d t} = 2 y + 1, y (0) = 0

y^{^{'}} = 3 y (1 - \frac{y}{6})

3 y + y^{^{'}} = 0

What is the solution for (dy)/(dx)=(y^2)/(sqrt(-x^2+100)) ?
The solution for (dy)/(dx)=(y^2)/(sqrt(-x^2+100)) is y=-1/(arcsin(1/10 x)+c_{1)}