23.3.107 problem 109

Internal problem ID [5821]
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 : 109
Date solved : Tuesday, September 30, 2025 at 02:03:43 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 41

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 \frac {1}{2} e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } c_1 \text {erfi}\left (\frac {x}{\sqrt {2}}\right )+2 c_2\right ) \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