Internal problem ID [9555]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1225.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve((x^2+1)*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\sqrt {x^{2}+1}\, c_{2} +x \left (c_{2} \operatorname {arcsinh}\left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 42
DSolve[y[x] - x*y'[x] + (1 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -c_2 \sqrt {x^2+1}-c_2 x \log \left (\sqrt {x^2+1}-x\right )+c_1 x \]