87.20.26 problem 27

Internal problem ID [23711]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 3. Linear Systems. Exercise at page 161
Problem number : 27
Date solved : Thursday, October 02, 2025 at 09:44:29 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=2 x+y \left (t \right )\\ y^{\prime }\left (t \right )&=-3 x+6 y \left (t \right ) \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 34

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

\begin{align*} x \left (t \right ) &= c_1 \,{\mathrm e}^{5 t}+c_2 \,{\mathrm e}^{3 t} \\ y \left (t \right ) &= 3 c_1 \,{\mathrm e}^{5 t}+c_2 \,{\mathrm e}^{3 t} \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 72

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

\begin{align*} x(t)&\to \frac {1}{2} e^{3 t} \left (c_2 \left (e^{2 t}-1\right )-c_1 \left (e^{2 t}-3\right )\right )\\ y(t)&\to -\frac {1}{2} e^{3 t} \left (3 c_1 \left (e^{2 t}-1\right )+c_2 \left (1-3 e^{2 t}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.058 (sec). Leaf size: 32

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(3*x(t) - 6*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

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