50.9.26 problem 5(b)

Internal problem ID [7962]
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 : 5(b)
Date solved : Monday, January 27, 2025 at 03:34:11 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(2*x^2*diff(y(x),x$2)+10*x*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} \ln \left (x \right )+c_{1}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 18

DSolve[2*x^2*D[y[x],{x,2}]+10*x*D[y[x],x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 c_2 \log (x)+c_1}{x^2} \]