74.12.5 problem 5

Internal problem ID [16312]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 09:02:43 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=2 t \,{\mathrm e}^{-2 t} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 26

dsolve(diff(y(t),t$2)+4*diff(y(t),t)+20*y(t)=2*t*exp(-2*t),y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-2 t} \left (8 \sin \left (4 t \right ) c_{2} +8 \cos \left (4 t \right ) c_{1} +t \right )}{8} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 32

DSolve[D[y[t],{t,2}]+4*D[y[t],t]+20*y[t]==2*t*Exp[-2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{8} e^{-2 t} (t+8 c_2 \cos (4 t)+8 c_1 \sin (4 t)) \]