23.3.114 problem 116

Internal problem ID [5828]
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 : 116
Date solved : Tuesday, September 30, 2025 at 02:03:48 PM
CAS classification : [_erf]

\begin{align*} -8 y+2 x y^{\prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 44

ode:=-8*y(x)+2*x*diff(y(x),x)+diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 36

ode=-8*y[x] + 2*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 c_1 e^{-x^2} \operatorname {HermiteH}(-5,x)+c_2 \left (\frac {4 x^4}{3}+4 x^2+1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*Derivative(y(x), x) - 8*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False