7.18.11 problem 11

Internal problem ID [540]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 4. Laplace transform methods. Section 4.2 (Transformation of initial value problems). Problems at page 287
Problem number : 11
Date solved : Saturday, March 29, 2025 at 04:56:13 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=2 x \left (t \right )+y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=6 x \left (t \right )+3 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: 0.024 (sec). Leaf size: 9

ode:=[diff(x(t),t) = 2*x(t)+y(t), diff(y(t),t) = 6*x(t)+3*y(t)]; 
ic:=x(0) = 1y(0) = -2; 
dsolve([ode,ic]);
 

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

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 10

ode={D[x[t],t]==2*x[t]+y[t],D[y[t],t]==6*x[t]+3*y[t]}; 
ic={x[0]==1,y[0]==-2}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to 1 \\ y(t)\to -2 \\ \end{align*}

✓ Sympy. Time used: 0.088 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-2*x(t) - y(t) + Derivative(x(t), t),0),Eq(-6*x(t) - 3*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = - \frac {C_{1}}{2} + \frac {C_{2} e^{5 t}}{3}, \ y{\left (t \right )} = C_{1} + C_{2} e^{5 t}\right ] \]