12.22.3 problem section 10.5, problem 3

Internal problem ID [2256]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 10 Linear system of Differential equations. Section 10.5, constant coefficient homogeneous system II. Page 555
Problem number : section 10.5, problem 3
Date solved : Tuesday, March 04, 2025 at 01:52:32 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}y_{1} \left (t \right )&=-7 y_{1} \left (t \right )+4 y_{2} \left (t \right )\\ \frac {d}{d t}y_{2} \left (t \right )&=-y_{1} \left (t \right )-11 y_{2} \left (t \right ) \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 34

ode:=[diff(y__1(t),t) = -7*y__1(t)+4*y__2(t), diff(y__2(t),t) = -y__1(t)-11*y__2(t)]; 
dsolve(ode);
 

\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{-9 t} \left (c_2 t +c_1 \right ) \\ y_{2} \left (t \right ) &= -\frac {{\mathrm e}^{-9 t} \left (2 c_2 t +2 c_1 -c_2 \right )}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 46

ode={D[ y1[t],t]==-7*y1[t]+4*y2[t],D[ y2[t],t]==-1*y1[t]-11*y2[t]}; 
ic={}; 
DSolve[{ode,ic},{y1[t],y2[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} \text {y1}(t)\to e^{-9 t} (2 c_1 t+4 c_2 t+c_1) \\ \text {y2}(t)\to e^{-9 t} (c_2-(c_1+2 c_2) t) \\ \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 41

from sympy import * 
t = symbols("t") 
y__1 = Function("y__1") 
y__2 = Function("y__2") 
ode=[Eq(7*y__1(t) - 4*y__2(t) + Derivative(y__1(t), t),0),Eq(y__1(t) + 11*y__2(t) + Derivative(y__2(t), t),0)] 
ics = {} 
dsolve(ode,func=[y__1(t),y__2(t)],ics=ics)
 

\[ \left [ y^{1}{\left (t \right )} = 2 C_{1} t e^{- 9 t} + \left (C_{1} + 2 C_{2}\right ) e^{- 9 t}, \ y^{2}{\left (t \right )} = - C_{1} t e^{- 9 t} - C_{2} e^{- 9 t}\right ] \]