60.3.157 problem 1161

Internal problem ID [11167]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1161
Date solved : Monday, January 27, 2025 at 10:47:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-(x+a)*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {BesselI}\left (2 \sqrt {a}, 2 \sqrt {x}\right )+c_{2} \operatorname {BesselK}\left (2 \sqrt {a}, 2 \sqrt {x}\right ) \]

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 78

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

\[ y(x)\to (-1)^{-\sqrt {a}} c_1 \operatorname {Gamma}\left (1-2 \sqrt {a}\right ) \operatorname {BesselI}\left (-2 \sqrt {a},2 \sqrt {x}\right )+(-1)^{\sqrt {a}} c_2 \operatorname {Gamma}\left (2 \sqrt {a}+1\right ) \operatorname {BesselI}\left (2 \sqrt {a},2 \sqrt {x}\right ) \]