Internal problem ID [10505]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 3, Laplace transform. Section 3.3 The convolution property. Exercises page
162
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }+3 x^{\prime }+2 x-{\mathrm e}^{-4 t}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve([diff(x(t),t$2)+3*diff(x(t),t)+2*x(t)=exp(-4*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\left ({\mathrm e}^{-3 t}-3 \,{\mathrm e}^{-t}+2\right ) {\mathrm e}^{-t}}{6} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 28
DSolve[{x''[t]+3*x'[t]+2*x[t]==Exp[-4*t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{6} e^{-4 t} \left (e^t-1\right )^2 \left (2 e^t+1\right ) \\ \end{align*}