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 = 0.0287546 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \tan ^{-1}\left (\frac {x}{\sqrt {-2 c_1-x^2}}\right )+c_2\right \},\left \{y(x)\to c_2-\tan ^{-1}\left (\frac {x}{\sqrt {-2 c_1-x^2}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.078 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) =-\arctan \left ( {x{\frac {1}{\sqrt {-{x}^{2}+{\it \_C1}}}}} \right ) +{\it \_C2},y \left ( x \right ) =\arctan \left ( {x{\frac {1}{\sqrt {-{x}^{2}+{\it \_C1}}}}} \right ) +{\it \_C2} \right \} \] 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),'implicit')
Maple raw output
y(x) = arctan(x/(-x^2+_C1)^(1/2))+_C2, y(x) = -arctan(x/(-x^2+_C1)^(1/2))+_C2