What is the solution for (dy}{dx}=\frac{x^2+1)/y ?

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

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(dy}{dx}=\frac{x^2+1)/y

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} = - \frac{x}{y e ^{x^{2}}}, y (0) = 1

\frac{d x}{d t} = 2 t x^{2}

y^{^{'}} = \frac{1 + y}{1 + x}

y y^{^{'}} = x - 2

\frac{d y}{d x} = (\frac{x}{y})^{2}

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