54.3.266 problem 1282

Internal problem ID [12561]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1282
Date solved : Wednesday, October 01, 2025 at 02:06:43 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

ode:=4*x^2*diff(diff(y(x),x),x)+4*x^3*diff(y(x),x)+(x^2+6)*(x^2-4)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-\frac {x^{2}}{4}} \left (c_2 \,x^{5}+c_1 \right )}{x^{2}} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 32

ode=(-4 + x^2)*(6 + 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 {e^{-\frac {x^2}{4}} \left (c_2 x^5+5 c_1\right )}{5 x^2} \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)) + (x**2 - 4)*(x**2 + 6)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False