What is the solution for yy^'=3((y^2-2)/(x^3))x^2 ?

The solution for yy^'=3((y^2-2)/(x^3))x^2 is y=sqrt(c_{1)x^6+2},y=-sqrt(c_{1)x^6+2}

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yy^'=3((y^2-2)/(x^3))x^2

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

y = c_{1} x^{6} + 2, y = - c_{1} x^{6} + 2

Solution steps

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

Solve separable ODE:

y = c_{1} x^{6} + 2, y = - c_{1} x^{6} + 2

y = c_{1} x^{6} + 2, y = - c_{1} x^{6} + 2

\frac{d}{d x} ((\frac{x + 9}{x - 9})^{5})

x \to - 6 - lim (\frac{x + 2}{x + 6})

\int \frac{9}{x ^{2} - 9 x} d x

\frac{x}{1 + x ^{2}}

\int a x^{2} d x

What is the solution for yy^'=3((y^2-2)/(x^3))x^2 ?
The solution for yy^'=3((y^2-2)/(x^3))x^2 is y=sqrt(c_{1)x^6+2},y=-sqrt(c_{1)x^6+2}