54.3.186 problem 1200

Internal problem ID [12481]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1200
Date solved : Friday, October 03, 2025 at 03:19:23 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

ode:=x^2*diff(diff(y(x),x),x)+2*x^2*diff(y(x),x)-v*(v-1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \sqrt {x}\, \left (\operatorname {BesselK}\left (v -\frac {1}{2}, x\right ) c_2 +\operatorname {BesselI}\left (v -\frac {1}{2}, x\right ) c_1 \right ) \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 45

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

\begin{align*} y(x)&\to e^{-x} \sqrt {x} \left (c_1 \operatorname {BesselJ}\left (v-\frac {1}{2},-i x\right )+c_2 \operatorname {BesselY}\left (v-\frac {1}{2},-i x\right )\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
v = symbols("v") 
y = Function("y") 
ode = Eq(-v*(v - 1)*y(x) + 2*x**2*Derivative(y(x), x) + x**2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None