38.1.3 problem 3

Internal problem ID [8164]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 05:16:22 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \end{align*}

✗ Maple

ode:=t^5*diff(diff(diff(diff(y(t),t),t),t),t)-t^3*diff(diff(y(t),t),t)+6*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 236

ode=t^5*D[y[t],{t,4}]-t^3*D[y[t],{t,2}]+6*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 6^{\frac {1}{2} \left (\sqrt {5}-5\right )} c_1 \left (\frac {1}{t}\right )^{\frac {1}{2} \left (\sqrt {5}-5\right )} \, _0F_3\left (;-\frac {3}{2}+\frac {\sqrt {5}}{2},-\frac {1}{2}+\frac {\sqrt {5}}{2},1+\sqrt {5};-\frac {6}{t}\right )+6^{-\frac {5}{2}-\frac {\sqrt {5}}{2}} c_2 \left (\frac {1}{t}\right )^{-\frac {5}{2}-\frac {\sqrt {5}}{2}} \, _0F_3\left (;1-\sqrt {5},-\frac {3}{2}-\frac {\sqrt {5}}{2},-\frac {1}{2}-\frac {\sqrt {5}}{2};-\frac {6}{t}\right )-c_3 \, _0F_3\left (;2,\frac {7}{2}-\frac {\sqrt {5}}{2},\frac {7}{2}+\frac {\sqrt {5}}{2};-\frac {6}{t}\right )+c_4 G_{0,4}^{2,0}\left (-\frac {6}{t}| \begin {array}{c} -1,0,\frac {1}{2} \left (-5-\sqrt {5}\right ),\frac {1}{2} \left (-5+\sqrt {5}\right ) \\ \end {array} \right ) \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**5*Derivative(y(t), (t, 4)) - t**3*Derivative(y(t), (t, 2)) + 6*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : solve: Cannot solve t**5*Derivative(y(t), (t, 4)) - t**3*Derivative(y(t), (t, 2)) + 6*y(t)