67.2.23 problem Problem 3(a)

Internal problem ID [13980]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 3(a)
Date solved : Tuesday, January 28, 2025 at 06:10:56 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 26

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

\[ y = c_{1} {\mathrm e}^{\left (-2+\sqrt {3}\right ) x}+c_{2} {\mathrm e}^{-\left (2+\sqrt {3}\right ) x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 34

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

\[ y(x)\to e^{-\left (\left (2+\sqrt {3}\right ) x\right )} \left (c_2 e^{2 \sqrt {3} x}+c_1\right ) \]