60.3.81 problem 1095

Internal problem ID [11077]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1095
Date solved : Wednesday, March 05, 2025 at 01:41:29 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

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

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

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

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

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

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

✓ Sympy. Time used: 0.197 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
l = symbols("l") 
y = Function("y") 
ode = Eq(l*x*y(x) + x*Derivative(y(x), (x, 2)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} J_{0}\left (\sqrt {l} x\right ) + C_{2} Y_{0}\left (\sqrt {l} x\right ) \]