Internal problem ID [179]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }+4 y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(4*diff(y(x),x$2)+4*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x}{2}}+c_{2} {\mathrm e}^{-\frac {x}{2}} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[4*y''[x]+4*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x/2} (c_2 x+c_1) \\ \end{align*}