74.11.17 problem 29

Internal problem ID [16267]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 08:59:28 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+26 y&=-338 t \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(diff(y(t),t$2)+2*diff(y(t),t)+26*y(t)=-338*t,y(t), singsol=all)
 

\[ y = {\mathrm e}^{-t} \sin \left (5 t \right ) c_{2} +\cos \left (5 t \right ) {\mathrm e}^{-t} c_{1} -13 t +1 \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 34

DSolve[D[y[t],{t,2}]+2*D[y[t],t]+26*y[t]==-338*t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -13 t+c_2 e^{-t} \cos (5 t)+c_1 e^{-t} \sin (5 t)+1 \]