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

The solution for (dy}{dx}=\frac{x^2+2)/y is y=sqrt((2x^3)/3+4x+c_{1)},y=-sqrt((2x^3)/3+4x+c_{1)}

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

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

y = \frac{2 x ^{3}}{3} + 4 x + c_{1}, y = - \frac{2 x ^{3}}{3} + 4 x + c_{1}

Solution steps

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

Solve separable ODE:

y = \frac{2 x ^{3}}{3} + 4 x + c_{1}, y = - \frac{2 x ^{3}}{3} + 4 x + c_{1}

y = \frac{2 x ^{3}}{3} + 4 x + c_{1}, y = - \frac{2 x ^{3}}{3} + 4 x + c_{1}

x \to - 3 lim (- 6)

(- 1.2) (- 5.2)

\int - 17 sin^{4} (x) cos (x) d x

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

5 x^{\frac{1}{3}} - 5 x^{- \frac{2}{3}}

What is the solution for (dy}{dx}=\frac{x^2+2)/y ?
The solution for (dy}{dx}=\frac{x^2+2)/y is y=sqrt((2x^3)/3+4x+c_{1)},y=-sqrt((2x^3)/3+4x+c_{1)}