ODE
\[ y(x) y''(x)=y'(x)^2+y(x) y'(x) \] ODE Classification
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0250834 (sec), leaf count = 16
\[\left \{\left \{y(x)\to c_2 e^{c_1 e^x}\right \}\right \}\]
Maple ✓
cpu = 0.092 (sec), leaf count = 15
\[ \left \{ \ln \left ( y \left ( x \right ) \right ) -{\it \_C1}\,{{\rm e}^{x}}-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[y[x]*y''[x] == y[x]*y'[x] + y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> E^(E^x*C[1])*C[2]}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+y(x)*diff(y(x),x), y(x),'implicit')
Maple raw output
ln(y(x))-_C1*exp(x)-_C2 = 0