Internal problem ID [13651]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-5 y^{\prime } x +29 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = x^{3} \left (c_{1} \sin \left (2 \sqrt {5}\, \ln \left (x \right )\right )+c_{2} \cos \left (2 \sqrt {5}\, \ln \left (x \right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 36
DSolve[x^2*y''[x]-5*x*y'[x]+29*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^3 \left (c_2 \cos \left (2 \sqrt {5} \log (x)\right )+c_1 \sin \left (2 \sqrt {5} \log (x)\right )\right ) \]