42.3.8 problem Example 3.37

Internal problem ID [8818]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page 181
Problem number : Example 3.37
Date solved : Tuesday, September 30, 2025 at 05:52:54 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

ode:=diff(diff(diff(diff(diff(y(t),t),t),t),t),t)-1/t*diff(diff(diff(diff(y(t),t),t),t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_4 \,t^{5}+c_5 \,t^{3}+c_3 \,t^{2}+c_2 t +c_1 \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 33

ode=D[ y[t],{t,5}]-1/t*D[y[t],{t,4}]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {c_1 t^5}{120}+c_5 t^3+c_4 t^2+c_3 t+c_2 \end{align*}

✓ Sympy. Time used: 0.052 (sec). Leaf size: 22

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

\[ y{\left (t \right )} = C_{1} + C_{2} t + C_{3} t^{2} + C_{4} t^{3} + C_{5} t^{5} \]