72.9.7 problem 7

Internal problem ID [14724]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Exercises section 3.1. page 258
Problem number : 7
Date solved : Thursday, March 13, 2025 at 04:16:30 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}p \left (t \right )&=3 p \left (t \right )-2 q \left (t \right )-7 r \left (t \right )\\ \frac {d}{d t}q \left (t \right )&=-2 p \left (t \right )+6 r \left (t \right )\\ \frac {d}{d t}r \left (t \right )&=\frac {73 q \left (t \right )}{100}+2 r \left (t \right ) \end{align*}

✓ Maple. Time used: 0.283 (sec). Leaf size: 912

ode:=[diff(p(t),t) = 3*p(t)-2*q(t)-7*r(t), diff(q(t),t) = -2*p(t)+6*r(t), diff(r(t),t) = 73/100*q(t)+2*r(t)]; 
dsolve(ode);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 602

ode={D[p[t],t]==3*p[t]-2*q[t]-7*r[t],D[ q[t],t]==-2*p[t]+6*r[t],D[r[t],t]==73/100*q[t]+2*r[t]}; 
ic={}; 
DSolve[{ode,ic},{p[t],q[t],r[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 14.995 (sec). Leaf size: 1663

from sympy import * 
t = symbols("t") 
p = Function("p") 
q = Function("q") 
r = Function("r") 
ode=[Eq(-3*p(t) + 2*q(t) + 7*r(t) + Derivative(p(t), t),0),Eq(2*p(t) - 6*r(t) + Derivative(q(t), t),0),Eq(-73*q(t)/100 - 2*r(t) + Derivative(r(t), t),0)] 
ics = {} 
dsolve(ode,func=[p(t),q(t),r(t)],ics=ics)
 

\[ \text {Solution too large to show} \]