85.70.2 problem 5 (b)

Internal problem ID [22926]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 6. Solution of linear differential equations by Laplace transform. A Exercises at page 283
Problem number : 5 (b)
Date solved : Thursday, October 02, 2025 at 09:16:41 PM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=-4 \\ \end{align*}

✓ Maple. Time used: 0.057 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.120 (sec). Leaf size: 14

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

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