12.22.16 problem section 10.5, problem 16

Internal problem ID [2269]
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 16
Date solved : Tuesday, March 04, 2025 at 01:52:45 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}y_{1} \left (t \right )&=-7 y_{1} \left (t \right )+24 y_{2} \left (t \right )\\ \frac {d}{d t}y_{2} \left (t \right )&=-6 y_{1} \left (t \right )+17 y_{2} \left (t \right ) \end{align*}

With initial conditions

\begin{align*} y_{1} \left (0\right ) = 3\\ y_{2} \left (0\right ) = 1 \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 28

ode:=[diff(y__1(t),t) = -7*y__1(t)+24*y__2(t), diff(y__2(t),t) = -6*y__1(t)+17*y__2(t)]; 
ic:=y__1(0) = 3y__2(0) = 1; 
dsolve([ode,ic]);
 

\begin{align*} y_{1} \left (t \right ) &= {\mathrm e}^{5 t} \left (-12 t +3\right ) \\ y_{2} \left (t \right ) &= \frac {{\mathrm e}^{5 t} \left (-144 t +24\right )}{24} \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 31

ode={D[ y1[t],t]==-7*y1[t]+24*y2[t],D[ y2[t],t]==-6*y1[t]+17*y2[t]}; 
ic={y1[0]==3,y2[0]==1}; 
DSolve[{ode,ic},{y1[t],y2[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} \text {y1}(t)\to -3 e^{5 t} (4 t-1) \\ \text {y2}(t)\to e^{5 t} (1-6 t) \\ \end{align*}

✓ Sympy. Time used: 0.106 (sec). Leaf size: 46

from sympy import * 
t = symbols("t") 
y__1 = Function("y__1") 
y__2 = Function("y__2") 
ode=[Eq(7*y__1(t) - 24*y__2(t) + Derivative(y__1(t), t),0),Eq(6*y__1(t) - 17*y__2(t) + Derivative(y__2(t), t),0)] 
ics = {} 
dsolve(ode,func=[y__1(t),y__2(t)],ics=ics)
 

\[ \left [ y^{1}{\left (t \right )} = - 12 C_{2} t e^{5 t} - \left (12 C_{1} - C_{2}\right ) e^{5 t}, \ y^{2}{\left (t \right )} = - 6 C_{1} e^{5 t} - 6 C_{2} t e^{5 t}\right ] \]