ODE
\[ x (3 y(x)+2 x) y'(x)+3 (y(x)+x)^2=0 \] ODE Classification
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.325485 (sec), leaf count = 71
\[\left \{\left \{y(x)\to -\frac {4 x^2+\sqrt {-2 x^4+6 e^{4 c_1}}}{6 x}\right \},\left \{y(x)\to \frac {-4 x^2+\sqrt {-2 x^4+6 e^{4 c_1}}}{6 x}\right \}\right \}\]
Maple ✓
cpu = 0.064 (sec), leaf count = 63
\[\left [y \left (x \right ) = \frac {-\frac {2 x^{2} \textit {\_C1}}{3}-\frac {\sqrt {-2 x^{4} \textit {\_C1}^{2}+6}}{6}}{\textit {\_C1} x}, y \left (x \right ) = \frac {-\frac {2 x^{2} \textit {\_C1}}{3}+\frac {\sqrt {-2 x^{4} \textit {\_C1}^{2}+6}}{6}}{\textit {\_C1} x}\right ]\] Mathematica raw input
DSolve[3*(x + y[x])^2 + x*(2*x + 3*y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/6*(4*x^2 + Sqrt[6*E^(4*C[1]) - 2*x^4])/x}, {y[x] -> (-4*x^2 + Sqrt[6*E^(4*C[1]) - 2*x^4])/(6*x)}}
Maple raw input
dsolve(x*(2*x+3*y(x))*diff(y(x),x)+3*(x+y(x))^2 = 0, y(x))
Maple raw output
[y(x) = (-2/3*x^2*_C1-1/6*(-2*_C1^2*x^4+6)^(1/2))/_C1/x, y(x) = (-2/3*x^2*_C1+1/6*(-2*_C1^2*x^4+6)^(1/2))/_C1/x]