14.21.11 problem Problem 11

Internal problem ID [3938]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4. page 689
Problem number : Problem 11
Date solved : Tuesday, September 30, 2025 at 06:59:15 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=36 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=12 \\ \end{align*}

✓ Maple. Time used: 0.107 (sec). Leaf size: 12

ode:=diff(diff(y(t),t),t)-diff(y(t),t)-12*y(t) = 36; 
ic:=[y(0) = 0, D(y)(0) = 12]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 3 \,{\mathrm e}^{4 t}-3 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 14

ode=D[y[t],{t,2}]-D[y[t],t]-12*y[t]==36; 
ic={y[0]==0,Derivative[1][y][0] ==12}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 3 \left (e^{4 t}-1\right ) \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-12*y(t) - Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 36,0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 12} 
dsolve(ode,func=y(t),ics=ics)
 

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