82.7.5 problem 34-7

Internal problem ID [21861]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 34. Simulataneous linear differential equations. Page 1118
Problem number : 34-7
Date solved : Thursday, October 02, 2025 at 08:03:01 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=4 x \left (t \right )-y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )+2 y \left (t \right ) \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 30

ode:=[diff(x(t),t) = 4*x(t)-y(t), diff(y(t),t) = x(t)+2*y(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \left (c_2 t +c_1 \right ) \\ y \left (t \right ) &= {\mathrm e}^{3 t} \left (c_2 t +c_1 -c_2 \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 44

ode={D[x[t],t]==4*x[t]-y[t],D[y[t],t]==x[t]+2*y[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^{3 t} (c_1 (t+1)-c_2 t)\\ y(t)&\to e^{3 t} ((c_1-c_2) t+c_2) \end{align*}

✓ Sympy. Time used: 0.055 (sec). Leaf size: 36

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

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