Internal problem ID [13646]
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 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {2 x^{2} y^{\prime \prime }-y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(2*x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sqrt {x}+c_{2} x \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 18
DSolve[2*x^2*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \sqrt {x}+c_2 x \]