What is the solution for x^2y^'+2xy=5y^3 ?

The solution for x^2y^'+2xy=5y^3 is y=sqrt(x/(2+c_{1)x^5)},y=-sqrt(x/(2+c_{1)x^5)}

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x^2y^'+2xy=5y^3

x^{2} y^{^{'}} + 2 x y = 5 y^{3}

y = \frac{x}{2 + c _{1} x ^{5}}, y = - \frac{x}{2 + c _{1} x ^{5}}

Solution steps

x^{2} y^{'} (x) + 2 x y = 5 y^{3}

Solve Bernoulli ODE:

y = \frac{x}{2 + c _{1} x ^{5}}, y = - \frac{x}{2 + c _{1} x ^{5}}

y = \frac{x}{2 + c _{1} x ^{5}}, y = - \frac{x}{2 + c _{1} x ^{5}}

(x^{2} + 1) \frac{d y}{d x} + 6 x (y - 1) = 0

y^{^{'}} = \frac{( x ^{2} + y )}{x + 1}

y^{^{'}} + \frac{y}{x} = x^{- 4}

s (t) = 14 + 15 sin (14 π t)

(x^{2} - 2 x y) d x + x d y = 0

What is the solution for x^2y^'+2xy=5y^3 ?
The solution for x^2y^'+2xy=5y^3 is y=sqrt(x/(2+c_{1)x^5)},y=-sqrt(x/(2+c_{1)x^5)}