Internal problem ID [5519]
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(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }-4 y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(2*diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x} \sin \relax (x )+c_{2} {\mathrm e}^{x} \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
DSolve[2*y''[x]-4*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (c_2 \cos (x)+c_1 \sin (x)) \\ \end{align*}