1.24.4 problem 14

Internal problem ID [604]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 5. Linear systems of differential equations. Section 5.3 (Matrices and linear systems). Problems at page 364
Problem number : 14
Date solved : Sunday, October 12, 2025 at 01:17:37 AM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 8.041 (sec). Leaf size: 3531

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

\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✗ Mathematica

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

Timed out

✗ Sympy

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

NotImplementedError :