63.9.13 problem 2(a)

Internal problem ID [13140]
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(a)
Date solved : Tuesday, January 28, 2025 at 05:06:19 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+7 x&=t \,{\mathrm e}^{3 t} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 32

dsolve(diff(x(t),t$2)+7*x(t)=t*exp(3*t),x(t), singsol=all)
 

\[ x \left (t \right ) = \sin \left (\sqrt {7}\, t \right ) c_{2} +\cos \left (\sqrt {7}\, t \right ) c_{1} +\frac {\left (8 t -3\right ) {\mathrm e}^{3 t}}{128} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 42

DSolve[D[x[t],{t,2}]+7*x[t]==t*Exp[3*t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{128} e^{3 t} (8 t-3)+c_1 \cos \left (\sqrt {7} t\right )+c_2 \sin \left (\sqrt {7} t\right ) \]