84.39.5 problem 27.5

Internal problem ID [22375]
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 : 27.5
Date solved : Sunday, October 12, 2025 at 05:52:21 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d^{2}}{d t^{2}}w \left (t \right )-y \left (t \right )+2 z \left (t \right )&=3 \,{\mathrm e}^{-t}\\ -2 \frac {d}{d t}w \left (t \right )+2 \frac {d}{d t}y \left (t \right )+z \left (t \right )&=0\\ 2 \frac {d}{d t}w \left (t \right )-2 y \left (t \right )+\frac {d}{d t}z \left (t \right )+2 \frac {d^{2}}{d t^{2}}z \left (t \right )&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ z \left (0\right )&=2 \\ D\left (z \right )\left (0\right )&=-2 \\ w \left (0\right )&=1 \\ D\left (w \right )\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 13.684 (sec). Leaf size: 49443

ode:=[diff(diff(w(t),t),t)-y(t)+2*z(t) = 3*exp(-t), -2*diff(w(t),t)+2*diff(y(t),t)+z(t) = 0, 2*diff(w(t),t)-2*y(t)+diff(z(t),t)+2*diff(diff(z(t),t),t) = 0]; 
ic:=[y(0) = 2, z(0) = 2, D(z)(0) = -2, w(0) = 1, D(w)(0) = 1]; 
dsolve([ode,op(ic)]);
 

\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ z \left (t \right ) &= -\frac {-215335183536 \,{\mathrm e}^{-t} \left (162+3 \sqrt {2913}\right )^{{4}/{3}} \sqrt {2913}-11622116838816 \,{\mathrm e}^{-t} \left (162+3 \sqrt {2913}\right )^{{4}/{3}}}{2376 \left (3887 \sqrt {2913}+209790\right ) \left (162+3 \sqrt {2913}\right )^{{4}/{3}} \left (54+\sqrt {2913}\right )^{2}} \\ \end{align*}

✓ Mathematica. Time used: 15.662 (sec). Leaf size: 7606394

ode={D[w[t],{t,2}]-y[t]+2*z[t]==3*Exp[-t],-2*D[w[t],t]+2*D[y[t],t]+z[t]==0,2*D[w[t],t]-2*y[t]+D[z[t],t]+2*D[z[t],{t,2}]==0}; 
ic={y[0]==2,z[0]==2,Derivative[1][z][0] ==-2,w[0]==1,Derivative[1][w][0] ==1}; 
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) + 2*z(t) + Derivative(w(t), (t, 2)) - 3*exp(-t),0),Eq(z(t) - 2*Derivative(w(t), t) + 2*Derivative(y(t), t),0),Eq(-2*y(t) + 2*Derivative(w(t), t) + Derivative(z(t), t) + 2*Derivative(z(t), (t, 2)),0)] 
ics = {y(0): 2, z(0): 2, Subs(Derivative(z(t), t), t, 0): -2, w(0): 1, Subs(Derivative(w(t), t), t, 0): 1} 
dsolve(ode,func=[y(t),z(t),w(t)],ics=ics)
 

Timed Out