73.17.12 problem 12

Internal problem ID [15546]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 08:01:45 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+\frac {5 y}{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(x^2*diff(y(x),x$2)+5/2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 32

DSolve[x^2*D[y[x],{x,2}]+5/2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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