60.3.288 problem 1305

Internal problem ID [11284]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1305
Date solved : Thursday, March 13, 2025 at 08:42:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime }+2 x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.063 (sec). Leaf size: 46

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

\[ y = \left (\operatorname {BesselK}\left (0, -\frac {1}{x}\right ) c_{2} -\operatorname {BesselK}\left (1, -\frac {1}{x}\right ) c_{2} +c_{1} \left (\operatorname {BesselI}\left (0, -\frac {1}{x}\right )+\operatorname {BesselI}\left (1, -\frac {1}{x}\right )\right )\right ) {\mathrm e}^{\frac {1}{x}} \]

✓ Mathematica. Time used: 0.199 (sec). Leaf size: 47

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

\[ y(x)\to c_2 G_{1,2}^{2,0}\left (-\frac {2}{x}| \begin {array}{c} \frac {1}{2} \\ -1,0 \\ \end {array} \right )+c_1 e^{\frac {1}{x}} \left (\operatorname {BesselI}\left (0,\frac {1}{x}\right )-\operatorname {BesselI}\left (1,\frac {1}{x}\right )\right ) \]

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**3*Derivative(y(x), (x, 2)) + y(x))/(2*x) cannot be solved by the factorable group method