84.39.2 problem 27.2

Internal problem ID [22372]
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. Solved problems. Page 164
Problem number : 27.2
Date solved : Thursday, October 02, 2025 at 08:38:02 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*} y \left (0\right )&=1 \\ z \left (0\right )&=1 \\ w \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 4.383 (sec). Leaf size: 456316

ode:=[diff(w(t),t)+y(t) = sin(t), diff(y(t),t)-z(t) = exp(t), diff(z(t),t)+w(t)+y(t) = 1]; 
ic:=[y(0) = 1, z(0) = 1, w(0) = 0]; 
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: 0.043 (sec). Leaf size: 3033

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

Too large to display

✗ Sympy

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

Timed Out