86.5.12 problem 12

Internal problem ID [23126]
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 : 12
Date solved : Thursday, October 02, 2025 at 09:23:08 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 12 x^{\prime \prime }-25 x^{\prime }+12 x&=0 \end{align*}

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

ode:=12*diff(diff(x(t),t),t)-25*diff(x(t),t)+12*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 \,{\mathrm e}^{\frac {3 t}{4}}+c_2 \,{\mathrm e}^{\frac {4 t}{3}} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 26

ode=12*D[x[t],{t,2}]-25*D[x[t],t]+12*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_1 e^{3 t/4}+c_2 e^{4 t/3} \end{align*}

✓ Sympy. Time used: 0.091 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(12*x(t) - 25*Derivative(x(t), t) + 12*Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} e^{\frac {3 t}{4}} + C_{2} e^{\frac {4 t}{3}} \]