90.16.4 problem 4

Internal problem ID [25262]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 4. Linear Constant Coefficient Differential Equations. Exercises at page 283
Problem number : 4
Date solved : Thursday, October 02, 2025 at 11:59:26 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\left (5\right )}+t y^{\prime \prime }-3 y&=0 \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Timed out

✗ Sympy

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

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