Internal problem ID [9444]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1114.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime } x -2 \left (x -1\right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 36
dsolve(x*diff(diff(y(x),x),x)-2*(x-1)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (\operatorname {BesselK}\left (0, -x \right ) c_{2} -\operatorname {BesselK}\left (1, -x \right ) c_{2} +c_{1} \left (\operatorname {BesselI}\left (0, -x \right )+\operatorname {BesselI}\left (1, -x \right )\right )\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.149 (sec). Leaf size: 39
DSolve[-y[x] - 2*(-1 + x)*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 G_{1,2}^{2,0}\left (-2 x\left | \begin {array}{c} \frac {1}{2} \\ -1,0 \\ \end {array} \right .\right )+c_1 e^x (\operatorname {BesselI}(0,x)-\operatorname {BesselI}(1,x)) \]