68.14.19 problem 19

Internal problem ID [17711]
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 : 19
Date solved : Thursday, October 02, 2025 at 02:27:16 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {{\mathrm e}^{t}}{t} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 32

ode:=diff(diff(diff(y(t),t),t),t)-3*diff(diff(y(t),t),t)+3*diff(y(t),t)-y(t) = 1/t*exp(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\left (2 \ln \left (t \right ) t^{2}+\left (4 c_3 -3\right ) t^{2}+4 c_2 t +4 c_1 \right ) {\mathrm e}^{t}}{4} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 39

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

\begin{align*} y(t)&\to \frac {1}{4} e^t \left (2 t^2 \log (t)+(-3+4 c_3) t^2+4 c_2 t+4 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.185 (sec). Leaf size: 19

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

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