57.1.9 problem 9

Internal problem ID [14314]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.1 First order equations. Exercises page 10
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:30:37 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 x^{\prime \prime }-5 x^{\prime }-3 x&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=2*diff(diff(x(t),t),t)-5*diff(x(t),t)-3*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 \,{\mathrm e}^{3 t}+c_2 \,{\mathrm e}^{-\frac {t}{2}} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 24

ode=2*D[x[t],{t,2}]-5*D[x[t],t]-3*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_1 e^{-t/2}+c_2 e^{3 t} \end{align*}

✓ Sympy. Time used: 0.091 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-3*x(t) - 5*Derivative(x(t), t) + 2*Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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