23.3.350 problem 353

Internal problem ID [6064]
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 : 353
Date solved : Tuesday, September 30, 2025 at 02:20:50 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 3 y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 27

ode:=3*y(x)+x*diff(y(x),x)+(-x^2+1)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 58

ode=3*y[x] + x*D[y[x],x] + (1 - x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \left (x^2-1\right )^{3/4} \left (c_2 Q_{\frac {3}{2}}^{\frac {3}{2}}(x)+\frac {\sqrt {\frac {2}{\pi }} c_1 x \left (2 x^2-3\right )}{\left (1-x^2\right )^{3/4}}\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + (1 - x**2)*Derivative(y(x), (x, 2)) + 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False