Internal problem ID [11445]
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 2.2.3 Complex eigenvalues. Exercises
page 94
Problem number: 1(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }-4 x^{\prime }+6 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 27
dsolve([diff(x(t),t$2)-4*diff(x(t),t)+6*x(t)=0,x(0) = 1, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{2 t} \left (-\sqrt {2}\, \sin \left (\sqrt {2}\, t \right )+\cos \left (\sqrt {2}\, t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 35
DSolve[{x''[t]-4*x'[t]+6*x[t]==0,{x[0]==1,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{2 t} \left (\cos \left (\sqrt {2} t\right )-\sqrt {2} \sin \left (\sqrt {2} t\right )\right ) \]