# Question:A strange bug, perhaps in dsolve

## Question:A strange bug, perhaps in dsolve

Maple 2019

Here is a strange one...

1> /Library/Frameworks/Maple.framework/Versions/2019/bin/maple ; exit;
|\^/|     Maple 2019 (APPLE UNIVERSAL OSX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019
<____ ____>  Waterloo Maple Inc.
|       Type ? for help.
> version();
User Interface: 1435526
Kernel: 1435526
Library: 1435526
1435526

> DE := (28*x + 44)*u(x) + (336*x^2 +
> 726*x - 12)*diff(u(x), x) + (144*x^3 + 396*x^2 - 9*x)*diff(u(x), x, x);
2               /d      \
DE := (28 x + 44) u(x) + (336 x  + 726 x - 12) |-- u(x)|
\dx     /

/ 2      \
3        2        |d       |
+ (144 x  + 396 x  - 9 x) |--- u(x)|
|  2     |
\dx      /

> dsolve({DE,u(0)=2},u(x));
memory used=21.5MB, alloc=44.3MB, time=0.37
memory used=53.3MB, alloc=84.3MB, time=0.94
Error, (in dsolve) when calling 'property/ConvertRelation'. Received: 'numeric
exception: division by zero'

Presumably, the solution should be

u0:=2*HeunG((11 - 5*sqrt(5))/(11 + 5*sqrt(5)), 352/(9*(11 + 5*sqrt(5))^3*(-11 + 5*sqrt(5))^2), 1/6, 7/6, 4/3, 1/2, -8*x/(11 + 5*sqrt(5)));

(I get that by replacing coefficient 44 in DE with variable e44, solve, then substitute back e44 = 44.)

But maybe the problem is that this solution turns out to be an algebraic function:

u1:=2^(7/6)/(1 - 22*x + sqrt(-16*x^2 - 44*x + 1))^(1/6);

﻿