12.22.6 problem section 10.5, problem 6

Internal problem ID [2259]
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 6
Date solved : Tuesday, March 04, 2025 at 01:52:35 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}y_{1} \left (t \right )&=-10 y_{1} \left (t \right )+9 y_{2} \left (t \right )\\ \frac {d}{d t}y_{2} \left (t \right )&=-4 y_{1} \left (t \right )+2 y_{2} \left (t \right ) \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 32

ode:=[diff(y__1(t),t) = -10*y__1(t)+9*y__2(t), diff(y__2(t),t) = -4*y__1(t)+2*y__2(t)]; 
dsolve(ode);
 

\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{-4 t} \left (c_2 t +c_1 \right ) \\ y_{2} \left (t \right ) &= \frac {{\mathrm e}^{-4 t} \left (6 c_2 t +6 c_1 +c_2 \right )}{9} \\ \end{align*}

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

ode={D[ y1[t],t]==-10*y1[t]+9*y2[t],D[ y2[t],t]==-4*y1[t]+2*y2[t]}; 
ic={}; 
DSolve[{ode,ic},{y1[t],y2[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} \text {y1}(t)\to e^{-4 t} (-6 c_1 t+9 c_2 t+c_1) \\ \text {y2}(t)\to e^{-4 t} (-4 c_1 t+6 c_2 t+c_2) \\ \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 46

from sympy import * 
t = symbols("t") 
y__1 = Function("y__1") 
y__2 = Function("y__2") 
ode=[Eq(10*y__1(t) - 9*y__2(t) + Derivative(y__1(t), t),0),Eq(4*y__1(t) - 2*y__2(t) + Derivative(y__2(t), t),0)] 
ics = {} 
dsolve(ode,func=[y__1(t),y__2(t)],ics=ics)
 

\[ \left [ y^{1}{\left (t \right )} = - 6 C_{2} t e^{- 4 t} - \left (6 C_{1} - C_{2}\right ) e^{- 4 t}, \ y^{2}{\left (t \right )} = - 4 C_{1} e^{- 4 t} - 4 C_{2} t e^{- 4 t}\right ] \]