85.91.2 problem 8 (b)

Internal problem ID [23048]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 11. Matrix eigenvalue methods for systems of linear differential equations. A Exercises at page 509
Problem number : 8 (b)
Date solved : Thursday, October 02, 2025 at 09:17:50 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )-x \left (t \right )+2 y \left (t \right )-z \left (t \right )&=t^{2}\\ \frac {d}{d t}y \left (t \right )+3 x \left (t \right )-y \left (t \right )+4 z \left (t \right )&={\mathrm e}^{t}\\ \frac {d}{d t}z \left (t \right )-2 x \left (t \right )+y \left (t \right )-z \left (t \right )&=0 \end{align*}

✓ Maple. Time used: 12.567 (sec). Leaf size: 11814

ode:=[diff(x(t),t)-x(t)+2*y(t)-z(t) = t^2, diff(y(t),t)+3*x(t)-y(t)+4*z(t) = exp(t), diff(z(t),t)-2*x(t)+y(t)-z(t) = 0]; 
dsolve(ode);
 

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

✓ Mathematica. Time used: 0.076 (sec). Leaf size: 2158

ode={D[x[t],{t,1}]-x[t]+2*y[t]-z[t]==t^2, D[y[t],{t,1}]+3*x[t]-y[t]+4*z[t]==Exp[t], D[z[t],t]-2*x[t]+y[t]-z[t]==0}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t],z[t]},t,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

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

Timed Out