84.40.2 problem 27.7

Internal problem ID [22377]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 27. Solutions of systems of linear differential equations with constant coefficients by Laplace transform. Supplementary problems
Problem number : 27.7
Date solved : Thursday, October 02, 2025 at 08:38:03 PM
CAS classification : system_of_ODEs

\begin{align*} y^{\prime }-z \left (t \right )&=0\\ y-z^{\prime }\left (t \right )&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ z \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 11

ode:=[diff(y(t),t)-z(t) = 0, y(t)-diff(z(t),t) = 0]; 
ic:=[y(0) = 1, z(0) = 1]; 
dsolve([ode,op(ic)]);
 

\begin{align*} y \left (t \right ) &= {\mathrm e}^{t} \\ z \left (t \right ) &= {\mathrm e}^{t} \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 14

ode={D[y[t],t]-z[t]==0,y[t]-D[z[t],t]==0}; 
ic={y[0]==1,z[0]==1}; 
DSolve[{ode,ic},{y[t],z[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^t\\ z(t)&\to e^t \end{align*}

✓ Sympy. Time used: 0.041 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
z = Function("z") 
ode=[Eq(-z(t) + Derivative(y(t), t),0),Eq(y(t) - Derivative(z(t), t),0)] 
ics = {y(0): 1, z(0): 1} 
dsolve(ode,func=[y(t),z(t)],ics=ics)
 

\[ \left [ y{\left (t \right )} = e^{t}, \ z{\left (t \right )} = e^{t}\right ] \]