Laplace Transform conundrum

Question

consider, x1(t) + constant = x2(t) => w/ laplace, X1(s) + c/s = X2(s) but, take the time derivative of the first equation, x1dot = x2dot => sX1(s) = sX2(s) => X1(s) = X2(s).

Which is correct?

Answer 1

When you have taken the transform of the differentiated equation, you have missed off constant terms. For the transform of the derivative is $$sX(s)-x(0)$$ You should find that the relation between you 2 functions then causes the original constant to be present, as one should expect.