65.6.8 problem 12.1 (viii)

Internal problem ID [13757]
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 (viii)
Date solved : Tuesday, January 28, 2025 at 06:02:04 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 z^{\prime \prime }+7 z^{\prime }-4 z&=0 \end{align*}

With initial conditions

\begin{align*} z \left (0\right )&=0\\ z^{\prime }\left (0\right )&=9 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 16

dsolve([2*diff(z(t),t$2)+7*diff(z(t),t)-4*z(t)=0,z(0) = 0, D(z)(0) = 9],z(t), singsol=all)
 

\[ z = 2 \left ({\mathrm e}^{\frac {9 t}{2}}-1\right ) {\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 49

DSolve[{D[z[t],{t,2}]+7*D[z[t],t]-4*z[t]==0,{z[0]==3,Derivative[1][z][0]==9}},z[t],t,IncludeSingularSolutions -> True]
 

\[ z(t)\to \frac {3}{10} e^{-\frac {1}{2} \left (7+\sqrt {65}\right ) t} \left (\left (5+\sqrt {65}\right ) e^{\sqrt {65} t}+5-\sqrt {65}\right ) \]