7.24.8 problem 18

Internal problem ID [608]
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 : 18
Date solved : Saturday, March 29, 2025 at 05:00:34 PM
CAS classification : system_of_ODEs

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError :