54.3.234 problem 1250

Internal problem ID [12529]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1250
Date solved : Wednesday, October 01, 2025 at 01:57:11 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 x y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 41

ode:=(-a^2+x^2)*diff(diff(y(x),x),x)+8*x*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.243 (sec). Leaf size: 91

ode=12*y[x] + 8*x*D[y[x],x] + (-a^2 + x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\exp \left (\int _1^x-\frac {3 a+K[1]}{a^2-K[1]^2}dK[1]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[2]}-\frac {3 a+K[1]}{a^2-K[1]^2}dK[1]\right )dK[2]+c_1\right )}{\left (a^2-x^2\right )^2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(8*x*Derivative(y(x), x) + (-a**2 + x**2)*Derivative(y(x), (x, 2)) + 12*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False