Internal problem ID [8807]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1227.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((x^2+1)*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} \left (x^{2}-1\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 21
DSolve[2*y[x] - 2*x*y'[x] + (1 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 x-c_1 (x-i)^2 \\ \end{align*}