Internal problem ID [4173]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter 1, Nature and meaning of a differential equation between two variables. page
12
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} x^{2}+c_{1} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 14
DSolve[x^2*y''[x]-2*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (c_2 x+c_1) \\ \end{align*}