74.14.19 problem 19

Internal problem ID [16424]
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 : Tuesday, January 28, 2025 at 09:07:49 AM
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*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 32

dsolve(diff(y(t),t$3)-3*diff(y(t),t$2)+3*diff(y(t),t)-y(t)=1/t*exp(t),y(t), singsol=all)
 

\[ y = \frac {\left (2 \ln \left (t \right ) t^{2}+\left (4 c_{3} -3\right ) t^{2}+4 c_{2} t +4 c_{1} \right ) {\mathrm e}^{t}}{4} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 39

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

\[ y(t)\to \frac {1}{4} e^t \left (2 t^2 \log (t)+(-3+4 c_3) t^2+4 c_2 t+4 c_1\right ) \]