ODE
\[ y(x) y''(x)=y(x)^2 y'(x)+y'(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.354287 (sec), leaf count = 31
\[\left \{\left \{y(x)\to -\frac {c_1 e^{c_1 (x+c_2)}}{-1+e^{c_1 (x+c_2)}}\right \}\right \}\]
Maple ✓
cpu = 2.198 (sec), leaf count = 28
\[\left [y \left (x \right ) = -\frac {\textit {\_C1} \,{\mathrm e}^{\textit {\_C2} \textit {\_C1}} {\mathrm e}^{\textit {\_C1} x}}{{\mathrm e}^{\textit {\_C2} \textit {\_C1}} {\mathrm e}^{\textit {\_C1} x}-1}\right ]\] Mathematica raw input
DSolve[y[x]*y''[x] == y[x]^2*y'[x] + y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -((E^(C[1]*(x + C[2]))*C[1])/(-1 + E^(C[1]*(x + C[2]))))}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+y(x)^2*diff(y(x),x), y(x))
Maple raw output
[y(x) = -_C1/(exp(_C2*_C1)*exp(_C1*x)-1)*exp(_C2*_C1)*exp(_C1*x)]