What is the solution for xy^2(dy)/(dx)=y^3+x^3,y(1)=5 ?

The solution for xy^2(dy)/(dx)=y^3+x^3,y(1)=5 is y=x\sqrt[3]{3ln(x)+125}

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xy^2(dy)/(dx)=y^3+x^3,y(1)=5

x y^{2} \frac{d y}{d x} = y^{3} + x^{3}, y (1) = 5

Solution steps

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

Solve Bernoulli ODE:

\frac{\partial}{\partial x} (\frac{2 x}{x - y})

5 t \cdot \frac{d y}{d t} + 2 y = t

y^{\frac{3}{2}} (y + c e^{y})

\frac{\partial}{\partial x} (\frac{a \cdot b}{c \cdot x})

\frac{d}{d x} ((x^{3} + 3)^{3})

What is the solution for xy^2(dy)/(dx)=y^3+x^3,y(1)=5 ?
The solution for xy^2(dy)/(dx)=y^3+x^3,y(1)=5 is y=x\sqrt[3]{3ln(x)+125}