ODE
\[ x^3+3 x (2 y(x)+x) y'(x)+3 y(x) (y(x)+2 x)=0 \] ODE Classification
[_exact, _rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Exact equation
Mathematica ✓
cpu = 0.0110045 (sec), leaf count = 75
\[\left \{\left \{y(x)\to -\frac {\sqrt {36 c_1 x-3 x^5+9 x^4}+3 x^2}{6 x}\right \},\left \{y(x)\to \frac {\sqrt {36 c_1 x-3 x^5+9 x^4}-3 x^2}{6 x}\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 24
\[ \left \{ {\frac {{x}^{4}}{4}}+3\,{x}^{2}y \left ( x \right ) +3\,x \left ( y \left ( x \right ) \right ) ^{2}+{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x^3 + 3*y[x]*(2*x + y[x]) + 3*x*(x + 2*y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(3*x^2 + Sqrt[9*x^4 - 3*x^5 + 36*x*C[1]])/(6*x)}, {y[x] -> (-3*x^2 + Sqrt[9*x^4 - 3*x^5 + 36*x*C[1]])/(6*x)}}
Maple raw input
dsolve(3*x*(x+2*y(x))*diff(y(x),x)+x^3+3*y(x)*(2*x+y(x)) = 0, y(x),'implicit')
Maple raw output
1/4*x^4+3*x^2*y(x)+3*x*y(x)^2+_C1 = 0