ODE
\[ \left (x^2+6 x y(x)+3\right ) y'(x)+3 y(x)^2+2 x y(x)+2 x=0 \] ODE Classification
[_exact, _rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Exact equation
Mathematica ✓
cpu = 0.011937 (sec), leaf count = 83
\[\left \{\left \{y(x)\to -\frac {\sqrt {36 c_1 x+x^4-12 x^3+6 x^2+9}+x^2+3}{6 x}\right \},\left \{y(x)\to -\frac {-\sqrt {36 c_1 x+x^4-12 x^3+6 x^2+9}+x^2+3}{6 x}\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 25
\[ \left \{ {x}^{2}y \left ( x \right ) +3\,x \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}+{\it \_C1}+3\,y \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[2*x + 2*x*y[x] + 3*y[x]^2 + (3 + x^2 + 6*x*y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(3 + x^2 + Sqrt[9 + 6*x^2 - 12*x^3 + x^4 + 36*x*C[1]])/(6*x)}, {y[x] -> -(3 + x^2 - Sqrt[9 + 6*x^2 - 12*x^3 + x^4 + 36*x*C[1]])/(6*x)}}
Maple raw input
dsolve((3+6*x*y(x)+x^2)*diff(y(x),x)+2*x+2*x*y(x)+3*y(x)^2 = 0, y(x),'implicit')
Maple raw output
x^2*y(x)+3*x*y(x)^2+x^2+_C1+3*y(x) = 0