ODE
\[ x (y(x)+x) y''(x)+x y'(x)^2+(x-y(x)) y'(x)=y(x) \] ODE Classification
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.204437 (sec), leaf count = 53
\[\left \{\left \{y(x)\to -x-\sqrt {(1+2 c_2) x^2+c_1}\right \},\left \{y(x)\to -x+\sqrt {(1+2 c_2) x^2+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.22 (sec), leaf count = 43
\[\left [y \left (x \right ) = -x -\sqrt {-\textit {\_C2} \,x^{2}+x^{2}+\textit {\_C1}}, y \left (x \right ) = -x +\sqrt {-\textit {\_C2} \,x^{2}+x^{2}+\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[(x - y[x])*y'[x] + x*y'[x]^2 + x*(x + y[x])*y''[x] == y[x],y[x],x]
Mathematica raw output
{{y[x] -> -x - Sqrt[C[1] + x^2*(1 + 2*C[2])]}, {y[x] -> -x + Sqrt[C[1] + x^2*(1 + 2*C[2])]}}
Maple raw input
dsolve(x*(x+y(x))*diff(diff(y(x),x),x)+x*diff(y(x),x)^2+(x-y(x))*diff(y(x),x) = y(x), y(x))
Maple raw output
[y(x) = -x-(-_C2*x^2+x^2+_C1)^(1/2), y(x) = -x+(-_C2*x^2+x^2+_C1)^(1/2)]