50.9.14 problem 1(n)

Internal problem ID [7950]
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(n)
Date solved : Monday, January 27, 2025 at 03:33:45 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 26

dsolve(4*diff(y(x),x$2)-8*diff(y(x),x)+7*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (c_{1} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{2} \cos \left (\frac {\sqrt {3}\, x}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 38

DSolve[4*D[y[x],{x,2}]-8*D[y[x],x]+7*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \]