ODE
\[ y(x) y''(x)=y'(x)^2+y(x)^2 \log (y(x)) \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0898975 (sec), leaf count = 63
\[\left \{\left \{y(x)\to e^{\frac {1}{2} \left (e^{c_2+x}-c_1 e^{-c_2-x}\right )}\right \},\left \{y(x)\to e^{\frac {1}{2} \left (e^{-c_2-x}-c_1 e^{c_2+x}\right )}\right \}\right \}\]
Maple ✓
cpu = 0.025 (sec), leaf count = 19
\[ \left \{ -{{\rm e}^{2\,x}}{\it \_C1}-2\,{{\rm e}^{x}}\ln \left ( y \left ( x \right ) \right ) +{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[y[x]*y''[x] == Log[y[x]]*y[x]^2 + y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> E^((E^(x + C[2]) - E^(-x - C[2])*C[1])/2)}, {y[x] -> E^((E^(-x - C[2]) - E^(x + C[2])*C[1])/2)}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+y(x)^2*ln(y(x)), y(x),'implicit')
Maple raw output
-exp(2*x)*_C1-2*exp(x)*ln(y(x))+_C2 = 0