Internal problem ID [11526]
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(i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }-2 x=1} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 23
dsolve([diff(x(t),t$2)-2*x(t)=1,x(0) = 1, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \frac {3 \,{\mathrm e}^{\sqrt {2}\, t}}{4}+\frac {3 \,{\mathrm e}^{-\sqrt {2}\, t}}{4}-\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 34
DSolve[{x''[t]-2*x[t]==1,{x[0]==1,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{4} \left (3 e^{-\sqrt {2} t}+3 e^{\sqrt {2} t}-2\right ) \]