60.3.110 problem 1114

Internal problem ID [11120]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1114
Date solved : Tuesday, January 28, 2025 at 05:41:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-y&=0 \end{align*}

✓ 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)
 

\[ y = {\mathrm e}^{x} \left (\operatorname {BesselK}\left (0, -x \right ) c_{2} -\operatorname {BesselK}\left (1, -x \right ) c_{2} +c_{1} \left (\operatorname {BesselI}\left (0, -x \right )+\operatorname {BesselI}\left (1, -x \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.173 (sec). Leaf size: 39

DSolve[-y[x] - 2*(-1 + x)*D[y[x],x] + x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 G_{1,2}^{2,0}\left (-2 x\left | \begin {array}{c} \frac {1}{2} \\ -1,0 \\ \end {array} \right .\right )+c_1 e^x (\operatorname {BesselI}(0,x)-\operatorname {BesselI}(1,x)) \]