73.13.9 problem 20.1 (i)

Internal problem ID [15387]
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 (i)
Date solved : Tuesday, January 28, 2025 at 07:54:05 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: 0.003 (sec). Leaf size: 29

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

\[ y = x^{3} \left (c_{1} \sin \left (2 \sqrt {5}\, \ln \left (x \right )\right )+c_{2} \cos \left (2 \sqrt {5}\, \ln \left (x \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 36

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

\[ y(x)\to x^3 \left (c_2 \cos \left (2 \sqrt {5} \log (x)\right )+c_1 \sin \left (2 \sqrt {5} \log (x)\right )\right ) \]