ODE
\[ y''(x)=x y'(x)^3 \] ODE Classification
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.253778 (sec), leaf count = 51
\[\left \{\left \{y(x)\to c_2-\tan ^{-1}\left (\frac {x}{\sqrt {-x^2-2 c_1}}\right )\right \},\left \{y(x)\to \tan ^{-1}\left (\frac {x}{\sqrt {-x^2-2 c_1}}\right )+c_2\right \}\right \}\]
Maple ✓
cpu = 0.277 (sec), leaf count = 37
\[\left [y \left (x \right ) = \arctan \left (\frac {x}{\sqrt {-x^{2}+\textit {\_C1}}}\right )+\textit {\_C2}, y \left (x \right ) = -\arctan \left (\frac {x}{\sqrt {-x^{2}+\textit {\_C1}}}\right )+\textit {\_C2}\right ]\] Mathematica raw input
DSolve[y''[x] == x*y'[x]^3,y[x],x]
Mathematica raw output
{{y[x] -> -ArcTan[x/Sqrt[-x^2 - 2*C[1]]] + C[2]}, {y[x] -> ArcTan[x/Sqrt[-x^2 - 2*C[1]]] + C[2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x) = x*diff(y(x),x)^3, y(x))
Maple raw output
[y(x) = arctan(x/(-x^2+_C1)^(1/2))+_C2, y(x) = -arctan(x/(-x^2+_C1)^(1/2))+_C2]