ODE
\[ x y''(x)=y'(x)^3+y'(x) \] ODE Classification
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0418983 (sec), leaf count = 67
\[\left \{\left \{y(x)\to c_2-i e^{-c_1} \sqrt {e^{2 c_1} x^2-1}\right \},\left \{y(x)\to c_2+i e^{-c_1} \sqrt {e^{2 c_1} x^2-1}\right \}\right \}\]
Maple ✓
cpu = 0.281 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) =-\sqrt {-{x}^{2}+{\it \_C1}}+{\it \_C2},y \left ( x \right ) =\sqrt {-{x}^{2}+{\it \_C1}}+{\it \_C2} \right \} \] Mathematica raw input
DSolve[x*y''[x] == y'[x] + y'[x]^3,y[x],x]
Mathematica raw output
{{y[x] -> ((-I)*Sqrt[-1 + E^(2*C[1])*x^2])/E^C[1] + C[2]}, {y[x] -> (I*Sqrt[-1 + E^(2*C[1])*x^2])/E^C[1] + C[2]}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x) = diff(y(x),x)^3+diff(y(x),x), y(x),'implicit')
Maple raw output
y(x) = -(-x^2+_C1)^(1/2)+_C2, y(x) = (-x^2+_C1)^(1/2)+_C2