77.9.3 problem 3

Internal problem ID [20446]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III(A) at page 31
Problem number : 3
Date solved : Thursday, October 02, 2025 at 06:02:59 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 x^{\prime \prime }+5 x^{\prime }-12 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)-12*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 \,{\mathrm e}^{-4 t}+c_2 \,{\mathrm e}^{\frac {3 t}{2}} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 24

ode=2*D[x[t],{t,2}]+5*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/2}+c_2 e^{-4 t} \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-12*x(t) + 5*Derivative(x(t), t) + 2*Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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