6.23.5 problem section 10.6, problem 5

Internal problem ID [2290]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 10 Linear system of Differential equations. Section 10.6, constant coefficient homogeneous system III. Page 566
Problem number : section 10.6, problem 5
Date solved : Tuesday, September 30, 2025 at 05:25:52 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}y_{1} \left (t \right )&=-3 y_{1} \left (t \right )-3 y_{2} \left (t \right )+y_{3} \left (t \right )\\ \frac {d}{d t}y_{2} \left (t \right )&=2 y_{2} \left (t \right )+2 y_{3} \left (t \right )\\ \frac {d}{d t}y_{3} \left (t \right )&=5 y_{1} \left (t \right )+y_{2} \left (t \right )+y_{3} \left (t \right ) \end{align*}

✓ Maple. Time used: 0.466 (sec). Leaf size: 1975

ode:=[diff(y__1(t),t) = -3*y__1(t)-3*y__2(t)+y__3(t), diff(y__2(t),t) = 2*y__2(t)+2*y__3(t), diff(y__3(t),t) = 5*y__1(t)+y__2(t)+y__3(t)]; 
dsolve(ode);
 

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 187

ode={D[ y1[t],t]==3*y1[t]-3*y2[t]+1*y3[t],D[ y2[t],t]==0*y1[t]+2*y2[t]+2*y3[t],D[ y3[t],t]==5*y1[t]+1*y2[t]+1*y3[t]}; 
ic={}; 
DSolve[{ode,ic},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} \text {y1}(t)&\to \frac {1}{4} e^{-2 t} \left ((3 c_1-c_2+c_3) e^{6 t} \cos (2 t)+(c_1-3 c_2-c_3) e^{6 t} \sin (2 t)+c_1+c_2-c_3\right )\\ \text {y2}(t)&\to \frac {1}{4} e^{-2 t} \left (-(c_1-3 c_2-c_3) e^{6 t} \cos (2 t)+(3 c_1-c_2+c_3) e^{6 t} \sin (2 t)+c_1+c_2-c_3\right )\\ \text {y3}(t)&\to \frac {1}{2} e^{-2 t} \left ((c_1+c_2+c_3) e^{6 t} \cos (2 t)+2 (c_1-c_2) e^{6 t} \sin (2 t)-c_1-c_2+c_3\right ) \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y__1 = Function("y__1") 
y__2 = Function("y__2") 
y__3 = Function("y__3") 
ode=[Eq(3*y__1(t) + 3*y__2(t) - y__3(t) + Derivative(y__1(t), t),0),Eq(-2*y__2(t) - 2*y__3(t) + Derivative(y__2(t), t),0),Eq(-5*y__1(t) - y__2(t) - y__3(t) + Derivative(y__3(t), t),0)] 
ics = {} 
dsolve(ode,func=[y__1(t),y__2(t),y__3(t)],ics=ics)
 

Timed Out