79.2.4 problem 5 (i)

Internal problem ID [18517]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 4. Autonomous systems. Exercises at page 69
Problem number : 5 (i)
Date solved : Tuesday, January 28, 2025 at 11:51:42 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-5 x^{\prime }+6 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(x(t),t$2)-5*diff(x(t),t)+6*x(t)=0,x(t), singsol=all)
 

\[ x = c_{1} {\mathrm e}^{2 t}+c_{2} {\mathrm e}^{3 t} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

DSolve[D[x[t],{t,2}]-5*D[x[t],t]+6*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{2 t} \left (c_2 e^t+c_1\right ) \]