14.21.1 problem Problem 1

Internal problem ID [3928]
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 1
Date solved : Tuesday, September 30, 2025 at 06:59:10 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-2 y&=6 \,{\mathrm e}^{5 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.106 (sec). Leaf size: 15

ode:=diff(y(t),t)-2*y(t) = 6*exp(5*t); 
ic:=[y(0) = 3]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = {\mathrm e}^{2 t}+2 \,{\mathrm e}^{5 t} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 18

ode=D[y[t],t]-2*y[t]==6*Exp[5*t]; 
ic={y[0]==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{2 t}+2 e^{5 t} \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) - 6*exp(5*t) + Derivative(y(t), t),0) 
ics = {y(0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (2 e^{3 t} + 1\right ) e^{2 t} \]