65.7.11 problem 14.1 (xi)

Internal problem ID [13775]
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 (xi)
Date solved : Tuesday, January 28, 2025 at 06:03:09 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&={\mathrm e}^{2 t} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(diff(x(t),t$2)+4*diff(x(t),t)+4*x(t)=exp(2*t),x(t), singsol=all)
 

\[ x \left (t \right ) = \left (c_{1} t +c_{2} \right ) {\mathrm e}^{-2 t}+\frac {{\mathrm e}^{2 t}}{16} \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 50

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

\[ x(t)\to \frac {1}{4} e^{-2 t} \left (4 \int _1^t-e^{4 K[1]} K[1]dK[1]+e^{4 t} t+4 (c_2 t+c_1)\right ) \]