68.14.18 problem 18

Internal problem ID [17710]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 18
Date solved : Thursday, October 02, 2025 at 02:27:16 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=-\frac {1}{t^{2}}-\frac {2}{t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=diff(diff(diff(y(t),t),t),t)-2*diff(diff(y(t),t),t) = -1/t^2-2/t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{2 t} c_1}{4}+t \ln \left (2\right )+t \ln \left (t \right )+\left (c_2 -1\right ) t +c_3 \]

✓ Mathematica. Time used: 0.109 (sec). Leaf size: 29

ode=D[ y[t],{t,3}]-2*D[y[t],{t,2}]==-1/t^2-2/t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t \log (t)+\frac {1}{4} c_1 e^{2 t}+(-1+c_3) t+c_2 \end{align*}

✓ Sympy. Time used: 0.176 (sec). Leaf size: 17

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

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