23.3.369 problem 373

Internal problem ID [6083]
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 : 373
Date solved : Tuesday, September 30, 2025 at 02:21:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 y-4 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=6*y(x)-4*x*diff(y(x),x)+(x^2+1)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{3}-3 c_1 \,x^{2}-3 c_2 x +c_1 \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 33

ode=6*y[x] - 4*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 -\frac {1}{3} i \left (c_2 \left (3 x^2-1\right )+3 c_1 (x-i)^3\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x*Derivative(y(x), x) + (x**2 + 1)*Derivative(y(x), (x, 2)) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False