63.9.2 problem 1(b)

Internal problem ID [13129]
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(b)
Date solved : Tuesday, January 28, 2025 at 04:54:19 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+x^{\prime }+x&=3 \cos \left (t \right )-2 \sin \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 39

dsolve(diff(x(t),t$2)+diff(x(t),t)+x(t)=3*cos(t)-2*sin(t),x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 56

DSolve[D[x[t],{t,2}]+D[x[t],t]+x[t]==3*Cos[t]-2*Sin[t],x[t],t,IncludeSingularSolutions -> True]
 

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