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 = 0.0802794 (sec), leaf count = 31
\[\left \{\left \{y(x)\to -\frac {c_1 e^{c_1 \left (c_2+x\right )}}{e^{c_1 \left (c_2+x\right )}-1}\right \}\right \}\]
Maple ✓
cpu = 0.067 (sec), leaf count = 25
\[ \left \{ -x-{\it \_C2}+{\frac {-\ln \left ( y \left ( x \right ) +{\it \_C1} \right ) +\ln \left ( y \left ( x \right ) \right ) }{{\it \_C1}}}=0 \right \} \] 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),'implicit')
Maple raw output
-x-_C2+(-ln(y(x)+_C1)+ln(y(x)))/_C1 = 0