ODE
\[ (x-y(x)) y''(x)+2 y'(x) \left (y'(x)+1\right )=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.563357 (sec), leaf count = 24
\[\left \{\left \{y(x)\to -\frac {e^{-c_1}}{x+c_2}-c_2\right \}\right \}\]
Maple ✓
cpu = 4.195 (sec), leaf count = 21
\[\left [y \left (x \right ) = \frac {\textit {\_C2}^{2}-\textit {\_C2} x +\textit {\_C1}}{\textit {\_C2} -x}\right ]\] Mathematica raw input
DSolve[2*y'[x]*(1 + y'[x]) + (x - y[x])*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -C[2] - 1/(E^C[1]*(x + C[2]))}}
Maple raw input
dsolve((x-y(x))*diff(diff(y(x),x),x)+2*diff(y(x),x)*(1+diff(y(x),x)) = 0, y(x))
Maple raw output
[y(x) = (_C2^2-_C2*x+_C1)/(_C2-x)]