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## Main Question or Discussion Point

I've been solving these two ODEs

##\frac{d}{d\,r}\,A=F(A,r) + \epsilon f(r)## and ##\frac{d}{d\,r}\,A=F(A,r)##.

If the solutions are respectively ##A_1(r,\epsilon)## and ##A_2(r)## then will ##A_1(r,0) = A_2(r)## ?

I realize the answer could depend on the actual functions but with the ones I'm using it appears that setting ##\epsilon=0## does not recover ##A_2##.

I'd be grateful for any advice on this.

##\frac{d}{d\,r}\,A=F(A,r) + \epsilon f(r)## and ##\frac{d}{d\,r}\,A=F(A,r)##.

If the solutions are respectively ##A_1(r,\epsilon)## and ##A_2(r)## then will ##A_1(r,0) = A_2(r)## ?

I realize the answer could depend on the actual functions but with the ones I'm using it appears that setting ##\epsilon=0## does not recover ##A_2##.

I'd be grateful for any advice on this.