63.9.3 problem 1(c)

Internal problem ID [13130]
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 : 1(c)
Date solved : Tuesday, January 28, 2025 at 04:55:35 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+x^{\prime }+x&=12 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 32

dsolve(diff(x(t),t$2)+diff(x(t),t)+x(t)=12,x(t), singsol=all)
 

\[ x \left (t \right ) = {\mathrm e}^{-\frac {t}{2}} \sin \left (\frac {\sqrt {3}\, t}{2}\right ) c_{2} +{\mathrm e}^{-\frac {t}{2}} \cos \left (\frac {\sqrt {3}\, t}{2}\right ) c_{1} +12 \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 49

DSolve[D[x[t],{t,2}]+D[x[t],t]+x[t]==12,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to c_2 e^{-t/2} \cos \left (\frac {\sqrt {3} t}{2}\right )+c_1 e^{-t/2} \sin \left (\frac {\sqrt {3} t}{2}\right )+12 \]