58.2.47 problem 47

Internal problem ID [9170]
Book : Second order enumerated odes
Section : section 2
Problem number : 47
Date solved : Tuesday, January 28, 2025 at 04:00:12 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 45

dsolve(diff(y(x),x$3)-x*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {hypergeom}\left (\left [\right ], \left [\frac {1}{2}, \frac {3}{4}\right ], \frac {x^{4}}{64}\right )+c_{2} x \operatorname {hypergeom}\left (\left [\right ], \left [\frac {3}{4}, \frac {5}{4}\right ], \frac {x^{4}}{64}\right )+c_3 \,x^{2} \operatorname {hypergeom}\left (\left [\right ], \left [\frac {5}{4}, \frac {3}{2}\right ], \frac {x^{4}}{64}\right ) \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 76

DSolve[D[y[x],{x,3}]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \, _0F_2\left (;\frac {1}{2},\frac {3}{4};\frac {x^4}{64}\right )+\frac {1}{8} x \left ((2+2 i) c_2 \, _0F_2\left (;\frac {3}{4},\frac {5}{4};\frac {x^4}{64}\right )+i c_3 x \, _0F_2\left (;\frac {5}{4},\frac {3}{2};\frac {x^4}{64}\right )\right ) \]