ODE
\[ y(x) y''(x)=-a y(x) y'(x)-b y(x)^2+y'(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0733805 (sec), leaf count = 28
\[\left \{\left \{y(x)\to c_2 e^{-\frac {c_1 e^{-a x}+b x}{a}}\right \}\right \}\]
Maple ✓
cpu = 0.038 (sec), leaf count = 27
\[ \left \{ -{{\rm e}^{-ax}}{\it \_C1}+bx+a\ln \left ( y \left ( x \right ) \right ) +{\it \_C2}-{\frac {b}{a}}=0 \right \} \] Mathematica raw input
DSolve[y[x]*y''[x] == -(b*y[x]^2) - a*y[x]*y'[x] + y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> C[2]/E^((b*x + C[1]/E^(a*x))/a)}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-a*y(x)*diff(y(x),x)-b*y(x)^2, y(x),'implicit')
Maple raw output
-exp(-a*x)*_C1+b*x+a*ln(y(x))+_C2-1/a*b = 0