76.13.21 problem 21

Internal problem ID [17603]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 10:45:06 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 18

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

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