82.7.14 problem 34-20

Internal problem ID [21870]
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 : 34-20
Date solved : Thursday, October 02, 2025 at 08:03:06 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 )-5 t\\ \frac {d}{d t}y \left (t \right )&=3 x \left (t \right )+6 y \left (t \right )-4 \end{align*}

✓ Maple. Time used: 0.044 (sec). Leaf size: 42

ode:=[diff(x(t),t) = 2*x(t)-y(t)-5*t, diff(y(t),t) = 3*x(t)+6*y(t)-4]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{5 t} c_2 +{\mathrm e}^{3 t} c_1 +2 t +1 \\ y \left (t \right ) &= -3 \,{\mathrm e}^{5 t} c_2 -{\mathrm e}^{3 t} c_1 -t \\ \end{align*}

✓ Mathematica. Time used: 0.161 (sec). Leaf size: 79

ode={D[x[t],t]==2*x[t]-y[t]-5*t,D[y[t],t]==3*x[t]+6*y[t]-4}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {1}{2} \left (4 t-(c_1+c_2) e^{5 t}+(3 c_1+c_2) e^{3 t}+2\right )\\ y(t)&\to -t+\frac {1}{2} e^{3 t} \left (3 c_1 \left (e^{2 t}-1\right )+c_2 \left (3 e^{2 t}-1\right )\right ) \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 39

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(5*t - 2*x(t) + y(t) + Derivative(x(t), t),0),Eq(-3*x(t) - 6*y(t) + Derivative(y(t), t) + 4,0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

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