Internal problem ID [12021]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {2 z^{\prime \prime }+7 z^{\prime }-4 z=0} \] With initial conditions \begin {align*} [z \left (0\right ) = 0, z^{\prime }\left (0\right ) = 9] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ z \left (t \right ) = 2 \left ({\mathrm e}^{\frac {9 t}{2}}-1\right ) {\mathrm e}^{-4 t} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 49
DSolve[{z''[t]+7*z'[t]-4*z[t]==0,{z[0]==3,z'[0]==9}},z[t],t,IncludeSingularSolutions -> True]
\[ z(t)\to \frac {3}{10} e^{-\frac {1}{2} \left (7+\sqrt {65}\right ) t} \left (\left (5+\sqrt {65}\right ) e^{\sqrt {65} t}+5-\sqrt {65}\right ) \]