23.3.481 problem 487

Internal problem ID [6195]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 487
Date solved : Friday, October 03, 2025 at 01:56:50 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 46

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

\[ y = \left (c_2 \operatorname {BesselK}\left (0, -\frac {1}{x}\right )-c_2 \operatorname {BesselK}\left (1, -\frac {1}{x}\right )+c_1 \left (\operatorname {BesselI}\left (0, -\frac {1}{x}\right )+\operatorname {BesselI}\left (1, -\frac {1}{x}\right )\right )\right ) {\mathrm e}^{\frac {1}{x}} \]

✓ Mathematica. Time used: 0.145 (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]
 

\begin{align*} 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 ) \end{align*}

✗ 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