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)]