Internal problem ID [9558]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1223.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -9 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve((x^2+1)*diff(diff(y(x),x),x)+x*diff(y(x),x)-9*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x \left (4 x^{2}+3\right ) c_{1} +\sqrt {x^{2}+1}\, \left (4 x^{2}+1\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 49
DSolve[-9*y[x] + x*y'[x] + (1 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cosh \left (3 \log \left (\sqrt {x^2+1}-x\right )\right )-i c_2 \sinh \left (3 \log \left (\sqrt {x^2+1}-x\right )\right ) \]