8.9.6 problem 6

Internal problem ID [850]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 6
Date solved : Monday, January 27, 2025 at 03:09:59 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+5*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{\frac {\left (-5+\sqrt {5}\right ) x}{2}}+c_2 \,{\mathrm e}^{-\frac {\left (5+\sqrt {5}\right ) x}{2}} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 35

DSolve[D[y[x],{x,2}]+5*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\frac {1}{2} \left (5+\sqrt {5}\right ) x} \left (c_2 e^{\sqrt {5} x}+c_1\right ) \]