65.7.4 problem 14.1 (iv)

Internal problem ID [13768]
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 (iv)
Date solved : Tuesday, January 28, 2025 at 06:02:28 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

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

\[ x \left (t \right ) = \frac {{\mathrm e}^{-2 t} \left (\left (t +3 c_{1} \right ) {\mathrm e}^{3 t}+3 c_{2} \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 29

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

\[ x(t)\to c_1 e^{-2 t}+e^t \left (\frac {t}{3}-\frac {1}{9}+c_2\right ) \]