50.14.4 problem 1(d)

Internal problem ID [8042]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:37:08 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {x}{2}} \left (c_{1} \sin \left (\frac {\sqrt {23}\, x}{2}\right )+c_{2} \cos \left (\frac {\sqrt {23}\, x}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 42

DSolve[D[y[x],{x,2}]-D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x/2} \left (c_2 \cos \left (\frac {\sqrt {23} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {23} x}{2}\right )\right ) \]