7.8.9 problem 9

Internal problem ID [223]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 9
Date solved : Monday, January 27, 2025 at 02:42:41 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 25

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

\[ y(x)\to 2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right ) \]