63.6.3 problem 1(c)

Internal problem ID [13114]
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 : 1(c)
Date solved : Tuesday, January 28, 2025 at 04:53:11 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} \frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2}&=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: 0.014 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

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

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

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