40.6.4 problem 4

Internal problem ID [8636]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 05:40:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+9 y&=10 \,{\mathrm e}^{-t} \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.118 (sec). Leaf size: 21

ode:=diff(diff(y(t),t),t)+9*y(t) = 10*exp(-t); 
ic:=[y(0) = 0, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 25

ode=D[y[t],{t,2}]+9*y[t]==10*Exp[-t]; 
ic={y[0]==0,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-t}+\frac {1}{3} \sin (3 t)-\cos (3 t) \end{align*}

✓ Sympy. Time used: 0.052 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(9*y(t) + Derivative(y(t), (t, 2)) - 10*exp(-t),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

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