60.3.91 problem 1095

Internal problem ID [11101]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1095
Date solved : Monday, January 27, 2025 at 10:45:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+y^{\prime }+l x y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(x*diff(diff(y(x),x),x)+diff(y(x),x)+l*x*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {BesselJ}\left (0, \sqrt {l}\, x \right )+c_{2} \operatorname {BesselY}\left (0, \sqrt {l}\, x \right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 30

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

\[ y(x)\to c_1 \operatorname {BesselJ}\left (0,\sqrt {l} x\right )+c_2 \operatorname {BesselY}\left (0,\sqrt {l} x\right ) \]