64.10.8 problem 8

Internal problem ID [13414]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 05:42:01 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

\[ y = {\mathrm e}^{-\frac {x}{2}} \left (c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 20

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

\[ y(x)\to e^{-x/2} (c_2 x+c_1) \]