Internal problem ID [13339]
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 (q).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {4 x^{2} y^{\prime \prime }+8 y^{\prime } x +5 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(4*x^2*diff(y(x),x$2)+8*x*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
\[ y = \frac {c_{1} \sin \left (\ln \left (x \right )\right )}{\sqrt {x}}+\frac {c_{2} \cos \left (\ln \left (x \right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 24
DSolve[4*x^2*y''[x]+8*x*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \cos (\log (x))+c_1 \sin (\log (x))}{\sqrt {x}} \]