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

The solution for xy^2(dy)/(dx)=y^3-3x^3,y(1)=5 is y=x\sqrt[3]{-9ln(x)+125}

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

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

y = x 3 - 9 ln (x) + 125

Solution steps

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

Solve Bernoulli ODE:

y = x 3 - 9 ln (x) + 125

y = x 3 - 9 ln (x) + 125

What is the solution for xy^2(dy)/(dx)=y^3-3x^3,y(1)=5 ?
The solution for xy^2(dy)/(dx)=y^3-3x^3,y(1)=5 is y=x\sqrt[3]{-9ln(x)+125}