85.70.5 problem 5 (e)

Internal problem ID [22929]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 6. Solution of linear differential equations by Laplace transform. A Exercises at page 283
Problem number : 5 (e)
Date solved : Thursday, October 02, 2025 at 09:16:42 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=100 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=20 \\ \end{align*}

✓ Maple. Time used: 0.079 (sec). Leaf size: 24

ode:=diff(diff(y(t),t),t)+8*diff(y(t),t)+25*y(t) = 100; 
ic:=[y(0) = 2, D(y)(0) = 20]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 4+\left (-2 \cos \left (3 t \right )+4 \sin \left (3 t \right )\right ) {\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 30

ode=D[y[t],{t,2}]+8*D[y[t],t]+25*y[t]==100; 
ic={y[0]==2,Derivative[1][y][0] ==20}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-4 t} \left (4 \left (e^{4 t}+\sin (3 t)\right )-2 \cos (3 t)\right ) \end{align*}

✓ Sympy. Time used: 0.145 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(25*y(t) + 8*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 100,0) 
ics = {y(0): 2, Subs(Derivative(y(t), t), t, 0): 20} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (4 \sin {\left (3 t \right )} - 2 \cos {\left (3 t \right )}\right ) e^{- 4 t} + 4 \]