14.21.14 problem Problem 14

Internal problem ID [3941]
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 14
Date solved : Tuesday, September 30, 2025 at 06:59:17 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=30 \,{\mathrm e}^{-3 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.096 (sec). Leaf size: 18

ode:=diff(diff(y(t),t),t)-2*diff(y(t),t) = 30*exp(-3*t); 
ic:=[y(0) = 1, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 2 \,{\mathrm e}^{-3 t}-4+3 \,{\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 21

ode=D[y[t],{t,2}]-2*D[y[t],t]==30*Exp[-3*t]; 
ic={y[0]==1,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.129 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 30*exp(-3*t),0) 
ics = {y(0): 1, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

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