Internal problem ID [10421]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 2, Second order linear equations. Section 2.2.2 Real eigenvalues. Exercises page
90
Problem number: 1(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+4 x^{\prime }+3 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(x(t),t$2)+4*diff(x(t),t)+3*x(t)=0,x(0) = 1, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \frac {3 \,{\mathrm e}^{-t}}{2}-\frac {{\mathrm e}^{-3 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[{x''[t]+4*x'[t]+3*x[t]==0,{x[0]==1,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-2 t} (2 \sinh (t)+\cosh (t)) \\ \end{align*}