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

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

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sqrt(1+x^3)(dy)/(dx)=x^2y+x^2

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

y = e^{\frac{2}{3} 1 + x^{3} + c_{1}} - 1

Solution steps

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

Solve separable ODE:

y = e^{\frac{2}{3} 1 + x^{3} + c_{1}} - 1

y = e^{\frac{2}{3} 1 + x^{3} + c_{1}} - 1

x \frac{d y}{d x} + y = 0

\frac{d y}{d x} = x^{4} (y - 4), y (0) = 8

y^{^{'}} = 0.1 y, y (0) = 8

\frac{d y}{d x} = \frac{x + 1}{2 - y}

e^{y} y^{^{'}} = 1

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