Internal problem ID [11520]
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(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }-x^{\prime }-6 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 2, x^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve([diff(x(t),t$2)-diff(x(t),t)-6*x(t)=0,x(0) = 2, D(x)(0) = -1],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\left (3 \,{\mathrm e}^{5 t}+7\right ) {\mathrm e}^{-2 t}}{5} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 23
DSolve[{x''[t]-x'[t]-6*x[t]==0,{x[0]==2,x'[0]==-1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{5} e^{-2 t} \left (3 e^{5 t}+7\right ) \]