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 = 0.00941262 (sec), leaf count = 65

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

Maple
cpu = 0.013 (sec), leaf count = 20

\[ \left \{ {x}^{3}y \relax (x ) -3\,{x}^{2}+ \left (y \relax (x ) \right ) ^{2}+{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

x^3*y(x)-3*x^2+y(x)^2+_C1 = 0