What is the solution for dyy^{-2}=(dx)/(sqrt(-x^2+144)) ?

The solution for dyy^{-2}=(dx)/(sqrt(-x^2+144)) is y=-1/(arcsin(1/12 x)+c_{1)}

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dyy^{-2}=(dx)/(sqrt(-x^2+144))

d y y^{- 2} = \frac{d x}{- x ^{2} + 144}

y = - \frac{1}{arcsin ( \frac{1}{12} x ) + c _{1}}

Solution steps

d y y^{- 2} = \frac{d x}{- x ^{2} + 144}

Solve separable ODE:

y = - \frac{1}{arcsin ( \frac{1}{12} x ) + c _{1}}

y = - \frac{1}{arcsin ( \frac{1}{12} x ) + c _{1}}

y = y^{^{'}} x

\frac{d y}{d x} = x^{5} (y - 5), y (0) = 8

(1 - x^{2}) y^{^{'}} - y^{2} = 0

\frac{d x}{d t} = 125 - \frac{x}{100}, x (0) = 4000

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

What is the solution for dyy^{-2}=(dx)/(sqrt(-x^2+144)) ?
The solution for dyy^{-2}=(dx)/(sqrt(-x^2+144)) is y=-1/(arcsin(1/12 x)+c_{1)}