Internal problem ID [13500]
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: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(4*x^2*diff(y(x),x$2)+8*x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y = \frac {c_{1}}{\sqrt {x}}+\frac {c_{2} \ln \left (x \right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 24
DSolve[4*x^2*y''[x]+8*x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \log (x)+2 c_1}{2 \sqrt {x}} \]