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 = 0.260409 (sec), leaf count = 28
\[\left \{\left \{y(x)\to c_2 e^{-\frac {b x+c_1 e^{-a x}}{a}}\right \}\right \}\]
Maple ✓
cpu = 2.542 (sec), leaf count = 39
\[\left [y \left (x \right ) = {\mathrm e}^{\frac {\textit {\_C1} \,{\mathrm e}^{-a x}}{a}} {\mathrm e}^{-\frac {b x}{a}} {\mathrm e}^{-\frac {\textit {\_C2}}{a}} {\mathrm e}^{\frac {b}{a^{2}}}\right ]\] 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))
Maple raw output
[y(x) = exp(1/a*_C1*exp(-a*x))/exp(1/a*b*x)/exp(1/a*_C2)*exp(b/a^2)]