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

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

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y^'=(x^2y+y^3)/(x^3)

y^{^{'}} = \frac{x ^{2} y + y ^{3}}{x ^{3}}

y = \frac{x}{- 2 ln ( x ) + c _{1}}, y = - \frac{x}{- 2 ln ( x ) + c _{1}}

Solution steps

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

Solve Bernoulli ODE:

y = \frac{x}{- 2 ln ( x ) + c _{1}}, y = - \frac{x}{- 2 ln ( x ) + c _{1}}

y = \frac{x}{- 2 ln ( x ) + c _{1}}, y = - \frac{x}{- 2 ln ( x ) + c _{1}}

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