79.2.6 problem 5 (iiI=i)

Internal problem ID [18519]
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 (iiI=i)
Date solved : Tuesday, January 28, 2025 at 11:51:45 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-4 x^{\prime }+5 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(diff(x(t),t$2)-4*diff(x(t),t)+5*x(t)=0,x(t), singsol=all)
 

\[ x = {\mathrm e}^{2 t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 22

DSolve[D[x[t],{t,2}]-4*D[x[t],t]+5*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

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