78.23.3 problem 3 (c)

Internal problem ID [18454]
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 : Tuesday, January 28, 2025 at 11:50:19 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*}

✓ Solution by Maple

Time used: 0.178 (sec). Leaf size: 14

dsolve([diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=2,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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