15.17.6 problem 6

Internal problem ID [3242]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 26, page 115
Problem number : 6
Date solved : Sunday, March 30, 2025 at 01:23:40 AM
CAS classification : system_of_ODEs

\begin{align*} 5 \frac {d}{d t}y \left (t \right )-3 \frac {d}{d t}x \left (t \right )-5 y \left (t \right )&=5 t\\ 3 \frac {d}{d t}x \left (t \right )-5 \frac {d}{d t}y \left (t \right )-2 x \left (t \right )&=0 \end{align*}

✓ Maple. Time used: 0.132 (sec). Leaf size: 27

ode:=[5*diff(y(t),t)-3*diff(x(t),t)-5*y(t) = 5*t, 3*diff(x(t),t)-5*diff(y(t),t)-2*x(t) = 0]; 
dsolve(ode);
 

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

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 43

ode={5*D[y[t],t]-3*D[x[t],t]-5*y[t]==5*t,3*D[x[t],t]-5*D[y[t],t]-2*x[t]==0}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to \frac {5}{6} \left (3+2 c_1 e^{2 t/5}\right ) \\ y(t)\to -t-\frac {2}{3} c_1 e^{2 t/5}-1 \\ \end{align*}

✗ Sympy

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