74.11.10 problem 22

Internal problem ID [16260]
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 : 22
Date solved : Tuesday, January 28, 2025 at 08:59:03 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=3 t \,{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 28

dsolve(diff(y(t),t$2)+4*y(t)=3*t*exp(-t),y(t), singsol=all)
 

\[ y = \sin \left (2 t \right ) c_{2} +\cos \left (2 t \right ) c_{1} +\frac {3 \left (5 t +2\right ) {\mathrm e}^{-t}}{25} \]

✓ Solution by Mathematica

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

DSolve[D[y[t],{t,2}]+4*y[t]==3*t*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {3}{25} e^{-t} (5 t+2)+c_1 \cos (2 t)+c_2 \sin (2 t) \]