Internal problem ID [6732]
Book: Second order enumerated odes
Section: section 2
Problem number: 47.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve(diff(y(x),x$3)-x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \hypergeom \left (\left [\right ], \left [\frac {1}{2}, \frac {3}{4}\right ], \frac {x^{4}}{64}\right )+c_{2} x \hypergeom \left (\left [\right ], \left [\frac {3}{4}, \frac {5}{4}\right ], \frac {x^{4}}{64}\right )+c_{3} x^{2} \hypergeom \left (\left [\right ], \left [\frac {5}{4}, \frac {3}{2}\right ], \frac {x^{4}}{64}\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 76
DSolve[y'''[x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \, _0F_2\left (;\frac {1}{2},\frac {3}{4};\frac {x^4}{64}\right )+\frac {1}{8} x \left ((2+2 i) c_2 \, _0F_2\left (;\frac {3}{4},\frac {5}{4};\frac {x^4}{64}\right )+i c_3 x \, _0F_2\left (;\frac {5}{4},\frac {3}{2};\frac {x^4}{64}\right )\right ) \\ \end{align*}