What is the solution for x^2*(dy)/(dx)=(-1)/(y^2),y(1)=2 ?

The solution for x^2*(dy)/(dx)=(-1)/(y^2),y(1)=2 is y=\sqrt[3]{3/x+5}

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x^2*(dy)/(dx)=(-1)/(y^2),y(1)=2

x^{2} \cdot \frac{d y}{d x} = \frac{- 1}{y ^{2}}, y (1) = 2

y = 3 \frac{3}{x} + 5

Solution steps

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

Solve separable ODE:

y = 3 \frac{3}{x} + 5

y = 3 \frac{3}{x} + 5

d x + x y d y = y^{2} d x + y d y, y (2) = 3

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

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

\frac{d}{d x} ((y - 3)^{2}) = 2 - (x - 1)^{2}

\frac{d}{df} (H (f)) = 3 u (f)^{2} f

What is the solution for x^2*(dy)/(dx)=(-1)/(y^2),y(1)=2 ?
The solution for x^2*(dy)/(dx)=(-1)/(y^2),y(1)=2 is y=\sqrt[3]{3/x+5}