Internal problem ID [11696]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number: 12.1 (iii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {z^{\prime \prime }-4 z^{\prime }+13 z=0} \] With initial conditions \begin {align*} [z \left (0\right ) = 7, z^{\prime }\left (0\right ) = 42] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([diff(z(t),t$2)-4*diff(z(t),t)+13*z(t)=0,z(0) = 7, D(z)(0) = 42],z(t), singsol=all)
\[ z \left (t \right ) = \frac {7 \,{\mathrm e}^{2 t} \left (4 \sin \left (3 t \right )+3 \cos \left (3 t \right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 27
DSolve[{z''[t]-4*z'[t]+13*z[t]==0,{z[0]==7,z'[0]==42}},z[t],t,IncludeSingularSolutions -> True]
\[ z(t)\to \frac {7}{3} e^{2 t} (4 \sin (3 t)+3 \cos (3 t)) \]