Internal problem ID [10454]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }-3 x^{\prime }-40 x-2 \,{\mathrm e}^{-t}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve([diff(x(t),t$2)-3*diff(x(t),t)-40*x(t)=2*exp(-t),x(0) = 0, D(x)(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = -\frac {\left (-22 \,{\mathrm e}^{13 t}+13 \,{\mathrm e}^{4 t}+9\right ) {\mathrm e}^{-5 t}}{234} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 30
DSolve[{x''[t]-3*x'[t]-40*x[t]==2*Exp[-t],{x[0]==0,x'[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{234} e^{-5 t} \left (-13 e^{4 t}+22 e^{13 t}-9\right ) \\ \end{align*}