65.7.5 problem 14.1 (v)

Internal problem ID [13769]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 14, Inhomogeneous second order linear equations. Exercises page 140
Problem number : 14.1 (v)
Date solved : Tuesday, January 28, 2025 at 06:02:30 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&={\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(diff(x(t),t$2)+2*diff(x(t),t)+x(t)=exp(-t),x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 27

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

\[ x(t)\to \frac {1}{2} e^{-t} \left (t^2+2 c_2 t+2 c_1\right ) \]