Internal problem ID [13334]
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 (L).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y = c_{1} \sin \left (\ln \left (x \right )\right )+c_{2} \cos \left (\ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 18
DSolve[x^2*y''[x]+x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos (\log (x))+c_2 \sin (\log (x)) \]