74.14.18 problem 18

Internal problem ID [16423]
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 : Tuesday, January 28, 2025 at 09:07:48 AM
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*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 29

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

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