50.9.4 problem 1(d)

Internal problem ID [7940]
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)
Date solved : Monday, January 27, 2025 at 03:33:23 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(2*diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

DSolve[2*D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (c_2 \cos (x)+c_1 \sin (x)) \]