23.3.108 problem 110

Internal problem ID [5822]
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 : 110
Date solved : Tuesday, September 30, 2025 at 02:03:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.07 (sec). Leaf size: 45

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

\begin{align*} y(x)&\to -\sqrt {\frac {\pi }{2}} c_2 x \text {erf}\left (\frac {x}{\sqrt {2}}\right )-c_2 e^{-\frac {x^2}{2}}+c_1 x \end{align*}

✗ Sympy

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

False