Internal problem ID [5522]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+2 y^{\prime }+3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(2*diff(y(x),x$2)+2*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {5}\, x}{2}\right )+c_{2} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {5}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 42
DSolve[2*y''[x]+2*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}