50.9.7 problem 1(g)

Internal problem ID [7943]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant Coefficients. Page 62
Problem number : 1(g)
Date solved : Monday, January 27, 2025 at 03:33:28 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }+3 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(2*diff(y(x),x$2)+2*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x}{2}} \left (c_{1} \sin \left (\frac {\sqrt {5}\, x}{2}\right )+c_{2} \cos \left (\frac {\sqrt {5}\, x}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 42

DSolve[2*D[y[x],{x,2}]+2*D[y[x],x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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