23.3.555 problem 562

Internal problem ID [6269]
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 : 562
Date solved : Tuesday, September 30, 2025 at 02:39:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y+2 x \left (a^{2}+2 x^{2}\right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }&=0 \end{align*}

✗ Maple

ode:=-(a4*x^4+a2*x^2+a0)*y(x)+2*x*(a^2+2*x^2)*diff(y(x),x)+(a^2+x^2)^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=-((a0 + a2*x^2 + a4*x^4)*y[x]) + 2*x*(a^2 + 2*x^2)*D[y[x],x] + (a^2 + x^2)^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
a0 = symbols("a0") 
a2 = symbols("a2") 
a4 = symbols("a4") 
y = Function("y") 
ode = Eq(2*x*(a**2 + 2*x**2)*Derivative(y(x), x) + (a**2 + x**2)**2*Derivative(y(x), (x, 2)) + (-a0 - a2*x**2 - a4*x**4)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False