12.8.19 problem 22

Internal problem ID [1755]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page 203
Problem number : 22
Date solved : Saturday, March 29, 2025 at 11:38:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.081 (sec). Leaf size: 32

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

\[ y = c_1 \operatorname {HeunB}\left (-\frac {1}{2}, -2, -\frac {1}{2}, 3, x +\frac {1}{2}\right )+c_2 \operatorname {HeunB}\left (\frac {1}{2}, -2, -\frac {1}{2}, 3, x +\frac {1}{2}\right ) \sqrt {4 x +2} \]

✗ Mathematica

ode=(2*x+1)*D[y[x],{x,2}]-2*(2*x^2-1)*D[y[x],x]-4*(x+1)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

False