ODE
\[ y''(x)+y'(x)^3+y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0633521 (sec), leaf count = 69
\[\left \{\left \{y(x)\to c_2-\tan ^{-1}\left (e^{-c_1} \sqrt {e^{2 x}-e^{2 c_1}}\right )\right \},\left \{y(x)\to \tan ^{-1}\left (e^{-c_1} \sqrt {e^{2 x}-e^{2 c_1}}\right )+c_2\right \}\right \}\]
Maple ✓
cpu = 0.237 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) =-\arctan \left ( \sqrt {{{\rm e}^{2\,x}}{\it \_C1}-1} \right ) +{\it \_C2},y \left ( x \right ) =\arctan \left ( \sqrt {{{\rm e}^{2\,x}}{\it \_C1}-1} \right ) +{\it \_C2} \right \} \] Mathematica raw input
DSolve[y'[x] + y'[x]^3 + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -ArcTan[Sqrt[E^(2*x) - E^(2*C[1])]/E^C[1]] + C[2]}, {y[x] -> ArcTan[Sqrt[E^(2*x) - E^(2*C[1])]/E^C[1]] + C[2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+diff(y(x),x)+diff(y(x),x)^3 = 0, y(x),'implicit')
Maple raw output
y(x) = arctan((exp(2*x)*_C1-1)^(1/2))+_C2, y(x) = -arctan((exp(2*x)*_C1-1)^(1/2))+_C2