7.22.7 problem 17

Internal problem ID [582]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 5. Linear systems of differential equations. Section 5.1 (First order systems and applications). Problems at page 335
Problem number : 17
Date solved : Saturday, March 29, 2025 at 04:57:14 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=6 x \left (t \right )-y \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 1\\ y \left (0\right ) = 2 \end{align*}

✓ Maple. Time used: 0.125 (sec). Leaf size: 17

ode:=[diff(x(t),t) = y(t), diff(y(t),t) = 6*x(t)-y(t)]; 
ic:=x(0) = 1y(0) = 2; 
dsolve([ode,ic]);
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{2 t} \\ y \left (t \right ) &= 2 \,{\mathrm e}^{2 t} \\ \end{align*}

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 20

ode={D[x[t],t]==y[t],D[y[t],t]==6*x[t]-y[t]}; 
ic={x[0]==1,y[0]==2}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to e^{2 t} \\ y(t)\to 2 e^{2 t} \\ \end{align*}

✓ Sympy. Time used: 0.132 (sec). Leaf size: 34

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-y(t) + Derivative(x(t), t),0),Eq(-6*x(t) + y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = - \frac {C_{1} e^{- 3 t}}{3} + \frac {C_{2} e^{2 t}}{2}, \ y{\left (t \right )} = C_{1} e^{- 3 t} + C_{2} e^{2 t}\right ] \]