Internal problem ID [11468]
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(e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }+x=9 \,{\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(x(t),t$2)+x(t)=9*exp(-t),x(t), singsol=all)
\[ x \left (t \right ) = \sin \left (t \right ) c_{2} +\cos \left (t \right ) c_{1} +\frac {9 \,{\mathrm e}^{-t}}{2} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 25
DSolve[x''[t]+x[t]==9*Exp[-t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {9 e^{-t}}{2}+c_1 \cos (t)+c_2 \sin (t) \]