1.24.7 problem 17

Internal problem ID [607]
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 : 17
Date solved : Tuesday, September 30, 2025 at 04:03:26 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+t\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )-3 z \left (t \right )+t^{2}\\ \frac {d}{d t}z \left (t \right )&=6 y \left (t \right )-7 z \left (t \right )+t^{3} \end{align*}

✓ Maple. Time used: 0.605 (sec). Leaf size: 3195

ode:=[diff(x(t),t) = 3*x(t)-4*y(t)+z(t)+t, diff(y(t),t) = x(t)-3*z(t)+t^2, diff(z(t),t) = 6*y(t)-7*z(t)+t^3]; 
dsolve(ode);
 

\begin{align*} \text {Expression too large to display} \\ y \left (t \right ) &= -\frac {5 t^{3}}{16}+\frac {465 t^{2}}{512}-\frac {5295 t}{8192}+\frac {14289}{262144}+c_1 \,{\mathrm e}^{-\frac {\left (3 \sqrt {16311}\, \left (386+3 \sqrt {16311}\right )^{{2}/{3}}-386 \left (386+3 \sqrt {16311}\right )^{{2}/{3}}-169 \left (386+3 \sqrt {16311}\right )^{{1}/{3}}+676\right ) t}{507}}+{\mathrm e}^{\frac {\left (3 \sqrt {16311}\, \left (386+3 \sqrt {16311}\right )^{{2}/{3}}-386 \left (386+3 \sqrt {16311}\right )^{{2}/{3}}-169 \left (386+3 \sqrt {16311}\right )^{{1}/{3}}-1352\right ) t}{1014}} c_2 \cos \left (\frac {\left (386+3 \sqrt {16311}\right )^{{1}/{3}} \left (386 \sqrt {3}\, \left (386+3 \sqrt {16311}\right )^{{1}/{3}}-9 \sqrt {5437}\, \left (386+3 \sqrt {16311}\right )^{{1}/{3}}-169 \sqrt {3}\right ) t}{1014}\right )+{\mathrm e}^{\frac {\left (3 \sqrt {16311}\, \left (386+3 \sqrt {16311}\right )^{{2}/{3}}-386 \left (386+3 \sqrt {16311}\right )^{{2}/{3}}-169 \left (386+3 \sqrt {16311}\right )^{{1}/{3}}-1352\right ) t}{1014}} c_3 \sin \left (\frac {\left (386+3 \sqrt {16311}\right )^{{1}/{3}} \left (386 \sqrt {3}\, \left (386+3 \sqrt {16311}\right )^{{1}/{3}}-9 \sqrt {5437}\, \left (386+3 \sqrt {16311}\right )^{{1}/{3}}-169 \sqrt {3}\right ) t}{1014}\right ) \\ \text {Expression too large to display} \\ \end{align*}

✓ Mathematica. Time used: 0.081 (sec). Leaf size: 2759

ode={D[x[t],t]==3*x[t]-4*y[t]+z[t]+t,D[y[t],t]==x[t]-3*z[t]+t^2,D[z[t],t]==6*y[t]-7*z[t]+t^3}; 
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 - 3*x(t) + 4*y(t) - z(t) + Derivative(x(t), t),0),Eq(-t**2 - x(t) + 3*z(t) + Derivative(y(t), t),0),Eq(-t**3 - 6*y(t) + 7*z(t) + Derivative(z(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
 

Timed Out