87.21.23 problem 23

Internal problem ID [23737]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 3. Linear Systems. Exercise at page 178
Problem number : 23
Date solved : Thursday, October 02, 2025 at 09:44:44 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=-10 x+y \left (t \right )+7 z \left (t \right )\\ y^{\prime }\left (t \right )&=-9 x+4 y \left (t \right )+5 z \left (t \right )\\ z^{\prime }\left (t \right )&=-17 x+y \left (t \right )+12 z \left (t \right ) \end{align*}

✓ Maple. Time used: 0.053 (sec). Leaf size: 67

ode:=[diff(x(t),t) = -10*x(t)+y(t)+7*z(t), diff(y(t),t) = -9*x(t)+4*y(t)+5*z(t), diff(z(t),t) = -17*x(t)+y(t)+12*z(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= c_1 \,{\mathrm e}^{2 t}+c_2 \,{\mathrm e}^{t}+c_3 \,{\mathrm e}^{3 t} \\ y \left (t \right ) &= \frac {c_1 \,{\mathrm e}^{2 t}}{3}+\frac {c_2 \,{\mathrm e}^{t}}{2}-c_3 \,{\mathrm e}^{3 t} \\ z \left (t \right ) &= \frac {5 c_1 \,{\mathrm e}^{2 t}}{3}+\frac {3 c_2 \,{\mathrm e}^{t}}{2}+2 c_3 \,{\mathrm e}^{3 t} \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 164

ode={D[x[t],t]==-10*x[t]+y[t]+7*z[t],D[y[t],t]==-9*x[t]+4*y[t]+5*z[t],D[z[t],t]==-17*x[t]+y[t]+12*z[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t],z[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^t \left (c_1 \left (-15 e^t+2 e^{2 t}+14\right )-\left (e^t-1\right ) \left (c_2 \left (e^t-2\right )+c_3 \left (e^t-8\right )\right )\right )\\ y(t)&\to e^t \left (c_1 \left (-5 e^t-2 e^{2 t}+7\right )+c_2 \left (e^t+e^{2 t}-1\right )+c_3 \left (3 e^t+e^{2 t}-4\right )\right )\\ z(t)&\to e^t \left (c_1 \left (-25 e^t+4 e^{2 t}+21\right )+c_2 \left (5 e^t-2 e^{2 t}-3\right )-c_3 \left (-15 e^t+2 e^{2 t}+12\right )\right ) \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
z = Function("z") 
ode=[Eq(10*x(t) - y(t) - 7*z(t) + Derivative(x(t), t),0),Eq(9*x(t) - 4*y(t) - 5*z(t) + Derivative(y(t), t),0),Eq(18*x(t) - y(t) - 12*z(t) + Derivative(z(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
 

Timed Out