76.24.3 problem 3

Internal problem ID [17723]
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 6.2 (Basic Theory of First Order Linear Systems). Problems at page 398
Problem number : 3
Date solved : Thursday, March 13, 2025 at 10:48:00 AM
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 }+7 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)+7*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}]+7*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(7*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 7*t**2*y(t) + t*(t - 1)*Derivative(y(t), (t, 4)) + exp(t)*Derivative(y(t), (t, 2))