63.9.14 problem 2(b)

Internal problem ID [13141]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.3.1 Nonhomogeneous Equations: Undetermined Coefficients. Exercises page 110
Problem number : 2(b)
Date solved : Tuesday, January 28, 2025 at 05:06:23 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{\prime \prime }-x^{\prime }&=6+{\mathrm e}^{2 t} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(diff(x(t),t$2)-diff(x(t),t)=6+exp(2*t),x(t), singsol=all)
 

\[ x \left (t \right ) = c_{1} {\mathrm e}^{t}+\frac {{\mathrm e}^{2 t}}{2}-6 t +c_{2} \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 26

DSolve[D[x[t],{t,2}]-D[x[t],t]==6+Exp[2*t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -6 t+\frac {e^{2 t}}{2}+c_1 e^t+c_2 \]