ODE
\[ y(x) y''(x)=y'(x)^2-2 y'(x) \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0274094 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {e^{c_1 \left (c_2+x\right )}-2}{c_1}\right \}\right \}\]
Maple ✓
cpu = 0.051 (sec), leaf count = 21
\[ \left \{ {\frac {\ln \left ( {\it \_C1}\,y \left ( x \right ) +2 \right ) }{{\it \_C1}}}-x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[y[x]*y''[x] == -2*y'[x] + y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (-2 + E^(C[1]*(x + C[2])))/C[1]}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-2*diff(y(x),x), y(x),'implicit')
Maple raw output
ln(_C1*y(x)+2)/_C1-x-_C2 = 0