73.13.11 problem 20.1 (k)

Internal problem ID [15389]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 20. Euler equations. Additional exercises page 382
Problem number : 20.1 (k)
Date solved : Tuesday, January 28, 2025 at 07:54:11 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+29 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+29*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \sin \left (5 \ln \left (x \right )\right )+c_{2} \cos \left (5 \ln \left (x \right )\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 26

DSolve[x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+29*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \cos (5 \log (x))+c_1 \sin (5 \log (x))}{x^2} \]