Internal problem ID [11453]
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: 3(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 ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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) = 2],x(t), singsol=all)
\[ x \left (t \right ) = -\frac {{\mathrm e}^{-t}}{2}-\frac {{\mathrm e}^{-3 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 21
DSolve[{x''[t]+4*x'[t]+3*x[t]==0,{x[0]==-1,x'[0]==2}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -\frac {1}{2} e^{-3 t} \left (e^{2 t}+1\right ) \]