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Question: Convert RootOf to radical

Question:Convert RootOf to radical

Oliveira 180 Maple 2019
radical dsolve rootof differential-equations
August 12 2019
1

In the DE solution below I cannot convert the RootOf function to radicals.
macro(solve = allvalues@solve);
_EnvExplicit := true;
de := x^4*diff(y(x), x $ 2) + omega^2*y(x) = 0;
bc := y(a) = 0, y(b) = 0, D(y)(a) = 1;
dsol := (dsolve({bc, de}, {omega, y(x)}) assuming (0 < a, a < b));
convert(dsol, radical);
{omega = RootOf(tan(_Z)*_Z*b*_C2 - sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(_Z*b*_C2/a) - arccos(_Z*b*_C2/a))*a)*b, y(x) = x*(-cos(RootOf(tan(_Z)*_Z*b*_C2 - sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(_Z*b*_C2/a) - arccos(_Z*b*_C2/a))*a)*b/x)*sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(RootOf(tan(_Z)*_Z*b*_C2 - sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(_Z*b*_C2/a) - arccos(_Z*b*_C2/a))*a)*b*_C2/a) - arccos(RootOf(tan(_Z)*_Z*b*_C2 - sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(_Z*b*_C2/a) - arccos(_Z*b*_C2/a))*a)*b*_C2/a))*a/(RootOf(tan(_Z)*_Z*b*_C2 - sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(_Z*b*_C2/a) - arccos(_Z*b*_C2/a))*a)*b) + sin(RootOf(tan(_Z)*_Z*b*_C2 - sin(-2*_B5*Pi + 2*Pi*_Z10 + 2*_B5*arccos(_Z*b*_C2/a) - arccos(_Z*b*_C2/a))*a)*b/x)*_C2)}

Does anyone know how to convert the above expression to radicals?
I'm grateful.
Oliveira
RootOf_to_radical.mw
 

In the DE solution below I cannot convert the RootOf function to radicals.

> 

macro(solve = `@`(allvalues, solve))
> 

_EnvExplicit := true
> 

de := x^4*(diff(y(x), `$`(x, 2)))+omega^2*y(x) = 0
> 

bc := y(a) = 0, y(b) = 0, (D(y))(a) = 1
> 

dsol := `assuming`([dsolve({bc, de}, {omega, y(x)})], [a > 0, b > a])
> 

convert(dsol, radical)

{omega = RootOf(tan(_Z)*_Z*b*_C2-sin(-2*_B5*Pi+2*Pi*_Z10+2*_B5*arccos(_Z*b*_C2/a)-arccos(_Z*b*_C2/a))*a)*b, y(x) = x*(-cos(RootOf(tan(_Z)*_Z*b*_C2-sin(-2*_B5*Pi+2*Pi*_Z10+2*_B5*arccos(_Z*b*_C2/a)-arccos(_Z*b*_C2/a))*a)*b/x)*sin(-2*_B5*Pi+2*Pi*_Z10+2*_B5*arccos(RootOf(tan(_Z)*_Z*b*_C2-sin(-2*_B5*Pi+2*Pi*_Z10+2*_B5*arccos(_Z*b*_C2/a)-arccos(_Z*b*_C2/a))*a)*b*_C2/a)-arccos(RootOf(tan(_Z)*_Z*b*_C2-sin(-2*_B5*Pi+2*Pi*_Z10+2*_B5*arccos(_Z*b*_C2/a)-arccos(_Z*b*_C2/a))*a)*b*_C2/a))*a/(RootOf(tan(_Z)*_Z*b*_C2-sin(-2*_B5*Pi+2*Pi*_Z10+2*_B5*arccos(_Z*b*_C2/a)-arccos(_Z*b*_C2/a))*a)*b)+sin(RootOf(tan(_Z)*_Z*b*_C2-sin(-2*_B5*Pi+2*Pi*_Z10+2*_B5*arccos(_Z*b*_C2/a)-arccos(_Z*b*_C2/a))*a)*b/x)*_C2)}

 (1)

Does anyone know how to convert the above expression to radicals?
I'm grateful.

Oliveira


 

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