Internal problem ID [13652]
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 (j).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +10 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+10*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x \left (c_{1} \sin \left (3 \ln \left (x \right )\right )+c_{2} \cos \left (3 \ln \left (x \right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 24
DSolve[x^2*y''[x]-x*y'[x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (c_2 \cos (3 \log (x))+c_1 \sin (3 \log (x))) \]