What is the solution for x^2dx-y(1+x^3)dy=0 ?

The solution for x^2dx-y(1+x^3)dy=0 is y=sqrt((2ln(1+x^3)+c_{1))/3},y=-sqrt((2ln(1+x^3)+c_{1))/3}

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x^2dx-y(1+x^3)dy=0

x^{2} d x - y (1 + x^{3}) d y = 0

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

Solution steps

x^{2} d x - y (1 + x^{3}) d y = 0

Solve separable ODE:

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

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

x \to 0 lim (\frac{x ^{5} + 3 x}{x})

\int z (a + b z^{3})^{2} d z

x \to 0 lim (\frac{1}{x cot ( x )})

y = x (4.2)

\int \frac{1}{n} sin (n t) d t

What is the solution for x^2dx-y(1+x^3)dy=0 ?
The solution for x^2dx-y(1+x^3)dy=0 is y=sqrt((2ln(1+x^3)+c_{1))/3},y=-sqrt((2ln(1+x^3)+c_{1))/3}