73.9.15 problem 14.2 (e)

Internal problem ID [15276]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.2 (e)
Date solved : Tuesday, January 28, 2025 at 07:51:28 AM
CAS classification : [[_Emden, _Fowler]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=\sqrt {x} \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,sqrt(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]
 

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