63.6.5 problem 3(a)

Internal problem ID [13116]
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 2.2.2 Real eigenvalues. Exercises page 90
Problem number : 3(a)
Date solved : Tuesday, January 28, 2025 at 04:53:15 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} x \left (0\right )&=-1\\ x^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 14

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

\[ x \left (t \right ) = {\mathrm e}^{2 t} \left (-1+4 t \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 16

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

\[ x(t)\to e^{2 t} (4 t-1) \]