65.6.3 problem 12.1 (iii)

Internal problem ID [13752]
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)
Date solved : Tuesday, January 28, 2025 at 06:01:51 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} z^{\prime \prime }-4 z^{\prime }+13 z&=0 \end{align*}

With initial conditions

\begin{align*} z \left (0\right )&=7\\ z^{\prime }\left (0\right )&=42 \end{align*}

✓ Solution by Maple

Time used: 0.034 (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)
 

\[ z = \frac {7 \,{\mathrm e}^{2 t} \left (4 \sin \left (3 t \right )+3 \cos \left (3 t \right )\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 27

DSolve[{D[z[t],{t,2}]-4*D[z[t],t]+13*z[t]==0,{z[0]==7,Derivative[1][z][0]==42}},z[t],t,IncludeSingularSolutions -> True]
 

\[ z(t)\to \frac {7}{3} e^{2 t} (4 \sin (3 t)+3 \cos (3 t)) \]