Hi,
So, I've come across a question which I thought I worked out correctly but my answer is way off so now I'm left confused. The question was:
dxdy=(x+1)(x+2)y and y=2, x=1
So I put the y terms on the LHS and the left the x terms on the RHS. I then split the fraction on the RHS. This gave me the following to integrate:
∫y1dy=∫x+11−x+21dxThis gave me the following:
ln|y| = ln|x+1| - ln|x+2| + c
c= ln|y| - ln|x+1| + ln|x+2|
c= ln|3| (when y=2, x=1, as given above).
Subbing this back into ln|y| = ln|x+1| - ln|x+2| + c gave me:
ln|y| = ln|x+1| - ln|x+2| + ln|3|
Raising everything to base e:
y=x+1 -(x+2) + 3
y=2
The correct answer is
y=x+23(x+1)When I took the approach of splitting the fraction, I was unsure if it was the correct thing to do, but I didn't know how else to approach the denominator.
Could anyone help?
Thanks
Marc