74.15.10 problem 10

Internal problem ID [16449]
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 : 10
Date solved : Tuesday, January 28, 2025 at 09:08:16 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 x^{2} y^{\prime \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)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 24

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

\[ y(x)\to \frac {1}{2} \sqrt {x} (c_2 \log (x)+2 c_1) \]