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 = 0.270077 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {-2+e^{c_1 (x+c_2)}}{c_1}\right \}\right \}\]
Maple ✓
cpu = 1.014 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {{\mathrm e}^{\textit {\_C2} \textit {\_C1}} {\mathrm e}^{\textit {\_C1} x}-2}{\textit {\_C1}}\right ]\] 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))
Maple raw output
[y(x) = (exp(_C2*_C1)*exp(_C1*x)-2)/_C1]