23.5.9 problem 9

Internal problem ID [6618]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 9
Date solved : Friday, October 03, 2025 at 02:09:37 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 45

ode:=diff(diff(diff(y(x),x),x),x) = x*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \operatorname {hypergeom}\left (\left [\right ], \left [\frac {1}{2}, \frac {3}{4}\right ], \frac {x^{4}}{64}\right )+c_2 x \operatorname {hypergeom}\left (\left [\right ], \left [\frac {3}{4}, \frac {5}{4}\right ], \frac {x^{4}}{64}\right )+c_3 \,x^{2} \operatorname {hypergeom}\left (\left [\right ], \left [\frac {5}{4}, \frac {3}{2}\right ], \frac {x^{4}}{64}\right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 76

ode=D[y[x],{x,3}] == x*y[x]; 
ic={}; 
DSolve[{ode,ic},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*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve -x*y(x) + Derivative(y(x), (x, 3))