I The constant value on the given exact differential equation

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chwala
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Does it matter where the constant is placed or is it placed accordingly for convenience? ...to avoid working with negative values?

Why not work with,

##y^2+(x^2+1)y-3x^3+k=0##

then,



##y^2+(x^2+1)y-3x^3=-k##

then proceed to apply the initial conditions?
My interest is on the highlighted part in red under exact_2 page.
 

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It's more natural to define a level surface of the conserved quantity as F(x,y) = C rather than F(x,y) = -C; the actual sign of C is of no consequence.

(The second alternative also introduces an additional minus sign, and therefore an increased risk of sign errors).
 
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pasmith said:
It's more natural to define a level surface of the conserved quantity as F(x,y) = C rather than F(x,y) = -C; the actual sign of C is of no consequence.

(The second alternative also introduces an additional minus sign, and therefore an increased risk of sign errors).
Thanks @pasmith . 'For convenience' as I put it...('more natural' as you put it)... or as Mathematicians like indicating 'more generally accepted...all these may apply. Cheers mate.
 
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