##### 4.10.26 $$\left (x^3+2 y(x)\right ) y'(x)=3 x (2-x y(x))$$

ODE
$\left (x^3+2 y(x)\right ) y'(x)=3 x (2-x y(x))$ ODE Classiﬁcation

[_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]]

Book solution method
Exact equation

Mathematica
cpu = 0.168426 (sec), leaf count = 65

$\left \{\left \{y(x)\to \frac {1}{2} \left (-x^3-\sqrt {x^6+12 x^2+4 c_1}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (-x^3+\sqrt {x^6+12 x^2+4 c_1}\right )\right \}\right \}$

Maple
cpu = 0.019 (sec), leaf count = 51

$\left [y \left (x \right ) = -\frac {x^{3}}{2}-\frac {\sqrt {x^{6}+12 x^{2}-4 \textit {\_C1}}}{2}, y \left (x \right ) = -\frac {x^{3}}{2}+\frac {\sqrt {x^{6}+12 x^{2}-4 \textit {\_C1}}}{2}\right ]$ Mathematica raw input

DSolve[(x^3 + 2*y[x])*y'[x] == 3*x*(2 - x*y[x]),y[x],x]

Mathematica raw output

{{y[x] -> (-x^3 - Sqrt[12*x^2 + x^6 + 4*C[1]])/2}, {y[x] -> (-x^3 + Sqrt[12*x^2
+ x^6 + 4*C[1]])/2}}

Maple raw input

dsolve((x^3+2*y(x))*diff(y(x),x) = 3*x*(2-x*y(x)), y(x))

Maple raw output

[y(x) = -1/2*x^3-1/2*(x^6+12*x^2-4*_C1)^(1/2), y(x) = -1/2*x^3+1/2*(x^6+12*x^2-4
*_C1)^(1/2)]