ODE
\[ 2 x y''(x)+y'(x)^3+y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.313765 (sec), leaf count = 59
\[\left \{\left \{y(x)\to c_2-2 i e^{c_1} \sqrt {-x+e^{2 c_1}}\right \},\left \{y(x)\to 2 i e^{c_1} \sqrt {-x+e^{2 c_1}}+c_2\right \}\right \}\]
Maple ✓
cpu = 0.372 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {2 \sqrt {\textit {\_C1} x -1}}{\textit {\_C1}}+\textit {\_C2}, y \left (x \right ) = -\frac {2 \sqrt {\textit {\_C1} x -1}}{\textit {\_C1}}+\textit {\_C2}\right ]\] Mathematica raw input
DSolve[y'[x] + y'[x]^3 + 2*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-2*I)*E^C[1]*Sqrt[E^(2*C[1]) - x] + C[2]}, {y[x] -> (2*I)*E^C[1]*Sqrt[E^(2*C[1]) - x] + C[2]}}
Maple raw input
dsolve(2*x*diff(diff(y(x),x),x)+diff(y(x),x)^3+diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = 2*(_C1*x-1)^(1/2)/_C1+_C2, y(x) = -2*(_C1*x-1)^(1/2)/_C1+_C2]