76.23.5 problem 6

Internal problem ID [17725]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 6. Systems of First Order Linear Equations. Section 6.1 (Definitions and examples). Problems at page 388
Problem number : 6
Date solved : Monday, March 31, 2025 at 04:26:04 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \end{align*}

✗ Maple

ode:=t*(t-1)*diff(diff(diff(diff(y(t),t),t),t),t)+exp(t)*diff(diff(y(t),t),t)+4*t^2*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=t*(t-1)*D[y[t],{t,4}]+Exp[t]*D[y[t],{t,2}]+4*t^2*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*t**2*y(t) + t*(t - 1)*Derivative(y(t), (t, 4)) + exp(t)*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : solve: Cannot solve 4*t**2*y(t) + t*(t - 1)*Derivative(y(t), (t, 4)) + exp(t)*Derivative(y(t), (t, 2))