Internal problem ID [13645]
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 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} x^{3}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 17
DSolve[x^2*y''[x]-2*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1 x^3}{3}+c_2 \]