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February 4

Derivative question

I have a problem that says:

${dy \over dx}+1=2y$

I've gone through the following:

$dy=2y-1dx$

$\int dy-2y=\int -dx$

$-y^{2}=-x$

This is not what my teacher got. Where have I gone wrong? It's something to do with moving the dx over to the right side, isn't it? It should be $(2y-1)dx$ shouldn't it? Yes, this is basic. But my answer works out for the rest of the problem, so it's messing with my brain at this hour. Thanks, Dismas|^(talk) 10:06, 4 February 2014 (UTC)[reply]

Yes it should be

dy=(2y-1)dx

. And then try getting all the y's on the left, division is your friend here. Plus you always get a constant added after integration. Dmcq (talk) 10:22, 4 February 2014 (UTC)[reply]

dy/dx+1=2y

dy=(2y−1)dx

d(2y−1)=2dy=2(2y−1)dx

d(2y−1)/(2y−1)=2dx

d(log(2y−1))=d(2x)

log(2y−1)=2x+K

2y−1=e^2x+K=e^2xe^K=Ae^2x

y=(1+Ae^2x)/2

Bo Jacoby (talk) 14:26, 4 February 2014 (UTC).[reply]