ODE
\[ 3 x^2+(2 x y(x)-x+3) y'(x)+y(x)^2-y(x)=0 \] ODE Classification
[_exact, _rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Exact equation
Mathematica ✓
cpu = 0.358854 (sec), leaf count = 75
\[\left \{\left \{y(x)\to -\frac {\sqrt {-4 x^4+x^2-6 x+4 c_1 x+9}-x+3}{2 x}\right \},\left \{y(x)\to \frac {\sqrt {-4 x^4+x^2+(-6+4 c_1) x+9}+x-3}{2 x}\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 63
\[\left [y \left (x \right ) = \frac {-3+x +\sqrt {-4 x^{4}-4 x \textit {\_C1} +x^{2}-6 x +9}}{2 x}, y \left (x \right ) = -\frac {3-x +\sqrt {-4 x^{4}-4 x \textit {\_C1} +x^{2}-6 x +9}}{2 x}\right ]\] Mathematica raw input
DSolve[3*x^2 - y[x] + y[x]^2 + (3 - x + 2*x*y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/2*(3 - x + Sqrt[9 - 6*x + x^2 - 4*x^4 + 4*x*C[1]])/x}, {y[x] -> (-3 + x + Sqrt[9 + x^2 - 4*x^4 + x*(-6 + 4*C[1])])/(2*x)}}
Maple raw input
dsolve((3-x+2*x*y(x))*diff(y(x),x)+3*x^2-y(x)+y(x)^2 = 0, y(x))
Maple raw output
[y(x) = 1/2/x*(-3+x+(-4*x^4-4*_C1*x+x^2-6*x+9)^(1/2)), y(x) = -1/2*(3-x+(-4*x^4-4*_C1*x+x^2-6*x+9)^(1/2))/x]