82.4.23 problem 28-23

Internal problem ID [21841]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 28. Laplace transforms. Page 850
Problem number : 28-23
Date solved : Thursday, October 02, 2025 at 08:02:45 PM
CAS classification : system_of_ODEs

\begin{align*} w^{\prime }\left (t \right )+y&=\sin \left (t \right )\\ y^{\prime }-z \left (t \right )&={\mathrm e}^{t}\\ w \left (t \right )+y+z^{\prime }\left (t \right )&=1 \end{align*}

With initial conditions

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

✓ Maple. Time used: 3.275 (sec). Leaf size: 323257

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

\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: 0.094 (sec). Leaf size: 3033

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

Too large to display

✗ Sympy

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

Timed Out