What is the solution for x^2y^'+xy=3y^3 ?

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

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x^2y^'+xy=3y^3

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

y = \frac{x}{2 + c _{1} x ^{3}}, y = - \frac{x}{2 + c _{1} x ^{3}}

Solution steps

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

Solve Bernoulli ODE:

y = \frac{x}{2 + c _{1} x ^{3}}, y = - \frac{x}{2 + c _{1} x ^{3}}

y = \frac{x}{2 + c _{1} x ^{3}}, y = - \frac{x}{2 + c _{1} x ^{3}}

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