Internal problem ID [5618]
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(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {\left (3+\sqrt {5}\right ) x}{2}}+c_{2} {\mathrm e}^{-\frac {\left (\sqrt {5}-3\right ) x}{2}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 35
DSolve[y''[x]-3*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\frac {1}{2} \left (\sqrt {5}-3\right ) x} \left (c_2 e^{\sqrt {5} x}+c_1\right ) \\ \end{align*}