82.7.3 problem 34-5

Internal problem ID [21859]
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 : 34-5
Date solved : Thursday, October 02, 2025 at 08:03:00 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 )&=-2 x \left (t \right )+3 y \left (t \right ) \end{align*}

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

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

\begin{align*} x \left (t \right ) &= c_1 \,{\mathrm e}^{t}+c_2 \,{\mathrm e}^{2 t} \\ y \left (t \right ) &= c_1 \,{\mathrm e}^{t}+2 c_2 \,{\mathrm e}^{2 t} \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 54

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

\begin{align*} x(t)&\to e^t \left (c_2 \left (e^t-1\right )-c_1 \left (e^t-2\right )\right )\\ y(t)&\to e^t \left (c_2 \left (2 e^t-1\right )-2 c_1 \left (e^t-1\right )\right ) \end{align*}

✓ Sympy. Time used: 0.044 (sec). Leaf size: 29

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

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