23.3.454 problem 459

Internal problem ID [6168]
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 : 459
Date solved : Tuesday, September 30, 2025 at 02:24:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} -\left (-2 x^{2}+3\right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=-(-2*x^2+3)*y(x)+4*x^3*diff(y(x),x)+4*x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-\frac {x^{2}}{2}} c_1 +c_2}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 26

ode=-((3 - 2*x^2)*y[x]) + 4*x^3*D[y[x],x] + 4*x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3*Derivative(y(x), x) + 4*x**2*Derivative(y(x), (x, 2)) + (2*x**2 - 3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False