Internal problem ID [11449]
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(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9}=0} \] 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([1/2*diff(x(t),t$2)+5/6*diff(x(t),t)+2/9*x(t)=0,x(0) = 1, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \frac {4 \,{\mathrm e}^{-\frac {t}{3}}}{3}-\frac {{\mathrm e}^{-\frac {4 t}{3}}}{3} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 23
DSolve[{1/2*x''[t]+5/6*x'[t]+2/9*x[t]==0,{x[0]==1,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{3} e^{-4 t/3} \left (4 e^t-1\right ) \]