Internal problem ID [11512]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 3, Laplace transform. Section 3.2.1 Initial value problems. Exercises page
156
Problem number: 6(e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }-2 x^{\prime }+2 x={\mathrm e}^{-t}} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 5.125 (sec). Leaf size: 24
dsolve([diff(x(t),t$2)-2*diff(x(t),t)+2*x(t)=exp(-t),x(0) = 0, D(x)(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{-t}}{5}+\frac {\left (-\cos \left (t \right )+7 \sin \left (t \right )\right ) {\mathrm e}^{t}}{5} \]
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 29
DSolve[{x''[t]-2*x'[t]+2*x[t]==Exp[-t],{x[0]==0,x'[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{5} \left (e^{-t}+7 e^t \sin (t)-e^t \cos (t)\right ) \]