85.49.8 problem 2 (b)

Internal problem ID [22809]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 194
Problem number : 2 (b)
Date solved : Thursday, October 02, 2025 at 09:14:49 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} s^{\prime \prime }-3 s^{\prime }+2 s&=8 t^{2}+12 \,{\mathrm e}^{-t} \end{align*}

With initial conditions

\begin{align*} s \left (0\right )&=0 \\ s^{\prime }\left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 30

ode:=diff(diff(s(t),t),t)-3*diff(s(t),t)+2*s(t) = 8*t^2+12*exp(-t); 
ic:=[s(0) = 0, D(s)(0) = 2]; 
dsolve([ode,op(ic)],s(t), singsol=all);
 

\[ s = 4 t^{2}+12 t +8 \,{\mathrm e}^{2 t}+2 \,{\mathrm e}^{-t}+14-24 \,{\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.211 (sec). Leaf size: 34

ode=D[s[t],{t,2}]-3*D[s[t],t]+2*s[t]==8*t^2+12*Exp[-t]; 
ic={s[0]==0,Derivative[1][s][0] ==0}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)&\to 2 \left (2 t^2+6 t+e^{-t}-11 e^t+3 e^{2 t}+7\right ) \end{align*}

✓ Sympy. Time used: 0.229 (sec). Leaf size: 65

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(-8*t**2 + 2*s(t) - 4*Derivative(s(t), t) + Derivative(s(t), (t, 2)) - 12*exp(-t),0) 
ics = {s(0): 0, Subs(Derivative(s(t), t), t, 0): 0} 
dsolve(ode,func=s(t),ics=ics)
 

\[ s{\left (t \right )} = 4 t^{2} + 16 t + \left (- \frac {79 \sqrt {2}}{7} - \frac {104}{7}\right ) e^{t \left (2 - \sqrt {2}\right )} + \left (- \frac {104}{7} + \frac {79 \sqrt {2}}{7}\right ) e^{t \left (\sqrt {2} + 2\right )} + 28 + \frac {12 e^{- t}}{7} \]