Internal problem ID [8694]
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]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve(x*diff(diff(y(x),x),x)-2*(x-1)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x} \left (\BesselI \left (0, -x \right )+\BesselI \left (1, -x \right )\right )+c_{2} {\mathrm e}^{x} \left (\BesselK \left (0, -x \right )-\BesselK \left (1, -x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 39
DSolve[-y[x] - 2*(-1 + x)*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 G_{1,2}^{2,0}\left (-2 x\left | {c} \frac {1}{2} \\ -1,0 \\ \\ \right .\right )+c_1 e^x (I_0(x)-I_1(x)) \\ \end{align*}