63.7.2 problem 1(b)

Internal problem ID [13121]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.2.3 Complex eigenvalues. Exercises page 94
Problem number : 1(b)
Date solved : Tuesday, January 28, 2025 at 04:53:27 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-4 x^{\prime }+6 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 27

dsolve([diff(x(t),t$2)-4*diff(x(t),t)+6*x(t)=0,x(0) = 1, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = {\mathrm e}^{2 t} \left (-\sqrt {2}\, \sin \left (\sqrt {2}\, t \right )+\cos \left (\sqrt {2}\, t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 35

DSolve[{D[x[t],{t,2}]-4*D[x[t],t]+6*x[t]==0,{x[0]==1,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{2 t} \left (\cos \left (\sqrt {2} t\right )-\sqrt {2} \sin \left (\sqrt {2} t\right )\right ) \]