73.11.23 problem 17.4 (e)

Internal problem ID [15337]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 17. Second order Homogeneous equations with constant coefficients. Additional exercises page 334
Problem number : 17.4 (e)
Date solved : Tuesday, January 28, 2025 at 07:53:00 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 10

dsolve([4*diff(y(x),x$2)+4*diff(y(x),x)+y(x)=0,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x}{2}} x \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 14

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

\[ y(x)\to e^{-x/2} x \]