74.22.13 problem 13

Internal problem ID [16589]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 13
Date solved : Monday, March 31, 2025 at 02:59:45 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-3 x^{\prime }+4 x&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(diff(x(t),t),t)-3*diff(x(t),t)+4*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = {\mathrm e}^{\frac {3 t}{2}} \left (c_1 \sin \left (\frac {\sqrt {7}\, t}{2}\right )+c_2 \cos \left (\frac {\sqrt {7}\, t}{2}\right )\right ) \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 42

ode=D[x[t],{t,2}]-3*D[x[t],t]+4*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to e^{3 t/2} \left (c_2 \cos \left (\frac {\sqrt {7} t}{2}\right )+c_1 \sin \left (\frac {\sqrt {7} t}{2}\right )\right ) \]

✓ Sympy. Time used: 0.163 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(4*x(t) - 3*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (C_{1} \sin {\left (\frac {\sqrt {7} t}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {7} t}{2} \right )}\right ) e^{\frac {3 t}{2}} \]