90.9.5 problem 37

Internal problem ID [25193]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 2. The Laplace Transform. Exercises at page 139
Problem number : 37
Date solved : Thursday, October 02, 2025 at 11:57:42 PM
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 )&=2 \\ y^{\prime }\left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.056 (sec). Leaf size: 17

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

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