54.3.85 problem 1099

Internal problem ID [12380]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1099
Date solved : Friday, October 03, 2025 at 03:18:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }-y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 25

ode:=x*diff(diff(y(x),x),x)-diff(y(x),x)+x^3*(exp(x^2)-v^2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \operatorname {BesselJ}\left (v , {\mathrm e}^{\frac {x^{2}}{2}}\right )+c_2 \operatorname {BesselY}\left (v , {\mathrm e}^{\frac {x^{2}}{2}}\right ) \]

✓ Mathematica. Time used: 0.398 (sec). Leaf size: 46

ode=x*D[y[x],{x,2}]-D[y[x],x]+x^3*(Exp[x^2]-v^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
v = symbols("v") 
y = Function("y") 
ode = Eq(x**3*(-v**2 + exp(x**2))*y(x) + x*Derivative(y(x), (x, 2)) - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False