ODE
\[ a x+b y(x)+y(x) y'(x)=0 \] ODE Classification
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.138588 (sec), leaf count = 71
\[\text {Solve}\left [\frac {1}{2} \log \left (a+\frac {b y(x)}{x}+\frac {y(x)^2}{x^2}\right )+\log (x)=\frac {b \tan ^{-1}\left (\frac {b+\frac {2 y(x)}{x}}{\sqrt {4 a-b^2}}\right )}{\sqrt {4 a-b^2}}+c_1,y(x)\right ]\]
Maple ✓
cpu = 0.016 (sec), leaf count = 67
\[ \left \{ -{\frac {1}{2}\ln \left ( {\frac {a{x}^{2}+bxy \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}} \right ) }-{b{\it Artanh} \left ( {\frac {bx+2\,y \left ( x \right ) }{x}{\frac {1}{\sqrt {{b}^{2}-4\,a}}}} \right ) {\frac {1}{\sqrt {{b}^{2}-4\,a}}}}-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[a*x + b*y[x] + y[x]*y'[x] == 0,y[x],x]
Mathematica raw output
Solve[Log[x] + Log[a + (b*y[x])/x + y[x]^2/x^2]/2 == (b*ArcTan[(b + (2*y[x])/x)/Sqrt[4*a - b^2]])/Sqrt[4*a - b^2] + C[1], y[x]]
Maple raw input
dsolve(y(x)*diff(y(x),x)+a*x+b*y(x) = 0, y(x),'implicit')
Maple raw output
-1/2*ln((a*x^2+b*x*y(x)+y(x)^2)/x^2)-b/(b^2-4*a)^(1/2)*arctanh((b*x+2*y(x))/x/(b^2-4*a)^(1/2))-ln(x)-_C1 = 0