Internal problem ID [10493]
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(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }-2 x^{\prime }+2 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve([diff(x(t),t$2)-2*diff(x(t),t)+2*x(t)=0,x(0) = 0, D(x)(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{t} \sin \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 11
DSolve[{x''[t]-2*x'[t]+2*x[t]==0,{x[0]==0,x'[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t \sin (t) \\ \end{align*}