60.3.145 problem 1149

Internal problem ID [11155]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1149
Date solved : Monday, January 27, 2025 at 10:47:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 45

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

\[ y = \left (\operatorname {BesselY}\left (\sqrt {1-4 b}, 2 \sqrt {a}\, \sqrt {x}\right ) c_{2} +\operatorname {BesselJ}\left (\sqrt {1-4 b}, 2 \sqrt {a}\, \sqrt {x}\right ) c_{1} \right ) \sqrt {x} \]

✓ Solution by Mathematica

Time used: 0.093 (sec). Leaf size: 95

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

\[ y(x)\to \sqrt {a} \sqrt {x} \left (c_1 \operatorname {Gamma}\left (1-\sqrt {1-4 b}\right ) \operatorname {BesselJ}\left (-\sqrt {1-4 b},2 \sqrt {a} \sqrt {x}\right )+c_2 \operatorname {Gamma}\left (\sqrt {1-4 b}+1\right ) \operatorname {BesselJ}\left (\sqrt {1-4 b},2 \sqrt {a} \sqrt {x}\right )\right ) \]