23.3.218 problem 220

Internal problem ID [5932]
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 : 220
Date solved : Tuesday, September 30, 2025 at 02:06:25 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 x y-\left (-x^{2}+4\right ) y^{\prime }+x y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 46

ode:=2*x*y(x)-(-x^2+4)*diff(y(x),x)+x*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{5} \left (\pi c_2 \,\operatorname {erf}\left (\frac {i \sqrt {2}\, x}{2}\right )+c_1 \right ) {\mathrm e}^{-\frac {x^{2}}{2}}-i \left (x^{4}+x^{2}+3\right ) c_2 \sqrt {2}\, \sqrt {\pi } \]

✓ Mathematica. Time used: 0.099 (sec). Leaf size: 68

ode=2*x*y[x] - (4 - x^2)*D[y[x],x] + x*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{30} \left (\sqrt {2 \pi } c_2 e^{-\frac {x^2}{2}} x^5 \text {erfi}\left (\frac {x}{\sqrt {2}}\right )+30 c_1 e^{-\frac {x^2}{2}} x^5-2 c_2 \left (x^4+x^2+3\right )\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x) + x*Derivative(y(x), (x, 2)) - (4 - x**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None