23.3.113 problem 115

Internal problem ID [5827]
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 : 115
Date solved : Tuesday, September 30, 2025 at 02:03:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 y-2 x y^{\prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 27

ode:=6*y(x)-2*x*diff(y(x),x)+diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \operatorname {hypergeom}\left (\left [-\frac {3}{2}\right ], \left [\frac {1}{2}\right ], x^{2}\right )+\frac {\left (-2 x^{3}+3 x \right ) c_1}{3} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 71

ode=6*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 \frac {1}{2} \sqrt {\pi } c_2 \sqrt {x^2} \left (2 x^2-3\right ) \text {erfi}\left (\sqrt {x^2}\right )+8 c_1 x^3-c_2 e^{x^2} x^2+c_2 e^{x^2}-12 c_1 x \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*Derivative(y(x), x) + 6*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False