74.15.9 problem 9

Internal problem ID [16448]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 09:08:14 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 24

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

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