Internal problem ID [8748]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1168.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}+2 x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+\frac {c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 15
DSolve[2*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\frac {c_1}{x} \\ \end{align*}