84.40.7 problem 27.13

Internal problem ID [22382]
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 : 27.13
Date solved : Sunday, October 12, 2025 at 05:52:22 AM
CAS classification :

\begin{align*} \frac {d^{2}}{d t^{2}}w \left (t \right )+y \left (t \right )+z \left (t \right )&=-1\\ w \left (t \right )+\frac {d^{2}}{d t^{2}}y \left (t \right )-z \left (t \right )&=0\\ -w \left (t \right )-\frac {d}{d t}y \left (t \right )+\frac {d^{2}}{d t^{2}}z \left (t \right )&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0 (sec). Leaf size: 0

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

✗ Mathematica

ode={D[w[t],{t,2}]+y[t]+z[t]==-1,w[t]+D[y[t],{t,2}]-z[t]==0,-w[t]-D[y[t],t]+D[z[t],{t,2}]==0}; 
ic={w[0]==0,Derivative[1][w][0] ==1,z[0]==-1,Derivative[1][z][0] ==1,y[0]==0,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},{w[t],z[t],y[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
w = Function("w") 
z = Function("z") 
y = Function("y") 
ode=[Eq(y(t) + z(t) + Derivative(w(t), (t, 2)) + 1,0),Eq(w(t) - z(t) + Derivative(y(t), (t, 2)),0),Eq(-w(t) - Derivative(y(t), t) + Derivative(z(t), (t, 2)),0)] 
ics = {w(0): 0, Subs(Derivative(w(t), t), t, 0): 1, z(0): -1, Subs(Derivative(z(t), t), t, 0): 1, y(0): 0, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=[w(t),z(t),y(t)],ics=ics)
 

ValueError : Exceeds the limit (4300 digits) for integer string conversion; use sys.set_int_max_str_digits() to increase the limit