57.2.1 problem 1

Internal problem ID [9055]
Book : First order enumerated odes
Section : section 2 (system of first order odes)
Problem number : 1
Date solved : Sunday, March 30, 2025 at 02:05:48 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )-x \left (t \right )&=y \left (t \right )+t\\ \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )&=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.148 (sec). Leaf size: 30

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

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

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 37

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

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

✗ Sympy

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