52.1.8 problem 6. direct method

Internal problem ID [8225]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. Section 6.2 SOLUTIONS ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number : 6. direct method
Date solved : Monday, January 27, 2025 at 03:46:25 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

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

\[ y = c_{1} +c_{2} {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 19

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

\[ y(x)\to c_2-\frac {1}{2} c_1 e^{-2 x} \]