78.23.3 problem 3 (c)

Internal problem ID [18375]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 9. Laplace transforms. Section 50. Applications to differential equations. Problems at page 462
Problem number : 3 (c)
Date solved : Thursday, March 13, 2025 at 11:55:11 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \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: 0.178 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+2*y(x) = 2; 
ic:=y(0) = 0, D(y)(0) = 1; 
dsolve([ode,ic],y(x),method='laplace');
 

\[ y = -{\mathrm e}^{-x} \cos \left (x \right )+1 \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 16

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

\[ y(x)\to 1-e^{-x} \cos (x) \]

✓ Sympy. Time used: 0.167 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = 1 - e^{- x} \cos {\left (x \right )} \]