65.6.11 problem 12.1 (xi)

Internal problem ID [13681]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number : 12.1 (xi)
Date solved : Wednesday, March 05, 2025 at 10:11:51 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 x^{\prime \prime }-20 x^{\prime }+21 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=-4\\ x^{\prime }\left (0\right )&=-12 \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 17

ode:=4*diff(diff(x(t),t),t)-20*diff(x(t),t)+21*x(t) = 0; 
ic:=x(0) = -4, D(x)(0) = -12; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x \left (t \right ) = -3 \,{\mathrm e}^{\frac {7 t}{2}}-{\mathrm e}^{\frac {3 t}{2}} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 23

ode=4*D[x[t],{t,2}]-20*D[x[t],t]+21*x[t]==0; 
ic={x[0]==-4,Derivative[1][x][0 ]==-12}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to -e^{3 t/2} \left (3 e^{2 t}+1\right ) \]

✓ Sympy. Time used: 0.180 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(21*x(t) - 20*Derivative(x(t), t) + 4*Derivative(x(t), (t, 2)),0) 
ics = {x(0): -4, Subs(Derivative(x(t), t), t, 0): -12} 
dsolve(ode,func=x(t),ics=ics)
 

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