86.5.5 problem 5

Internal problem ID [23119]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5a at page 74
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:23:05 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 x^{\prime \prime }+19 x^{\prime }-14 x&=0 \end{align*}

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

ode:=3*diff(diff(x(t),t),t)+19*diff(x(t),t)-14*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 \,{\mathrm e}^{-7 t}+c_2 \,{\mathrm e}^{\frac {2 t}{3}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 35

ode=D[x[t],{t,2}]+19*D[x[t],t]-14*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^{-\frac {1}{2} \left (19+\sqrt {417}\right ) t} \left (c_2 e^{\sqrt {417} t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-14*x(t) + 19*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} e^{\frac {t \left (-19 + \sqrt {417}\right )}{2}} + C_{2} e^{- \frac {t \left (19 + \sqrt {417}\right )}{2}} \]