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Using SageMath version 8.9, Release Date: 2019-09-29

MWE:

x = var('x')
y = function('y')
desolve(diff(y(x),x,2) + y(x) == 1, y(x),show_method=True,algorithm='maxima')

Gives

[_K2*cos(x) + _K1*sin(x) + 1, 'variationofparameters']

But

desolve(diff(y(x),x,2) + y(x) == 1, y(x),show_method=True,algorithm='fricas')

Gives

_C0*cos(x) + cos(x)^2 + _C1*sin(x) + sin(x)^2

Why show_method=True has no effect when using fricas algorithm?

is it supposed to work only with default algorithm which I assume uses maxima? This was not clear from the document shown here http://doc.sagemath.org/html/en/reference/calculus/sage/calculus/desolvers.html

Thanks --Nasser