14.21.10 problem Problem 10

Internal problem ID [3937]
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 10
Date solved : Tuesday, September 30, 2025 at 06:59:15 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.098 (sec). Leaf size: 16

ode:=diff(diff(y(t),t),t)-3*diff(y(t),t)+2*y(t) = 4; 
ic:=[y(0) = 0, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 2-5 \,{\mathrm e}^{t}+3 \,{\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 19

ode=D[y[t],{t,2}]-3*D[y[t],t]+2*y[t]==4; 
ic={y[0]==0,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -5 e^t+3 e^{2 t}+2 \end{align*}

✓ Sympy. Time used: 0.101 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*y(t) - 3*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 4,0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 3 e^{2 t} - 5 e^{t} + 2 \]