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 = 0.0357044 (sec), leaf count = 59
\[\left \{\left \{y(x)\to c_2-2 i e^{c_1} \sqrt {e^{2 c_1}-x}\right \},\left \{y(x)\to c_2+2 i e^{c_1} \sqrt {e^{2 c_1}-x}\right \}\right \}\]
Maple ✓
cpu = 0.271 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) =-2\,{\frac {\sqrt {{\it \_C1}\,x-1}}{{\it \_C1}}}+{\it \_C2},y \left ( x \right ) =2\,{\frac {\sqrt {{\it \_C1}\,x-1}}{{\it \_C1}}}+{\it \_C2} \right \} \] 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),'implicit')
Maple raw output
y(x) = 2*(_C1*x-1)^(1/2)/_C1+_C2, y(x) = -2*(_C1*x-1)^(1/2)/_C1+_C2