63.6.6 problem 3(b)

Internal problem ID [13046]
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(b)
Date solved : Monday, March 31, 2025 at 07:32:42 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-2 x^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.043 (sec). Leaf size: 10

ode:=diff(diff(x(t),t),t)-2*diff(x(t),t) = 0; 
ic:=x(0) = -1, D(x)(0) = 2; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x = -2+{\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 12

ode=D[x[t],{t,2}]-2*D[x[t],t]==0; 
ic={x[0]==-1,Derivative[1][x][0 ]==2}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.142 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-2*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): -1, Subs(Derivative(x(t), t), t, 0): 2} 
dsolve(ode,func=x(t),ics=ics)
 

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