7.8.26 problem 39

Internal problem ID [240]
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 : 39
Date solved : Monday, January 27, 2025 at 02:42:53 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: 0.003 (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]
 

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