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Differential equation question

Hi guys,Could someone help me with finding the solution to dy/dx = x + xy (You don't need to make y the subject) The answer is ln (1+y) = x^2/2 +c I can see how the answer is the above (using differentiation) but can't seem to find how to go the other way. Thanks!!
You can rewrite x+xyx+xy as x(1+y)x(1+y). Do you know where to go from there?
(edited 7 years ago)
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dyuunn
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Original post by NeverLucky
You can rewrite x+xyasx(1+y) x+xy as x(1+y). Do you know where to go from there?


Oh my goodness, I just saw it. I would separate the variables into
1/(1+y) . dy = x . dx

and then integrate each side to get
ln (1+y) = x^2/2 + c

Thank you for your help! By the way, how did you format the equations so it looks nicer? :smile:
Original post by dyuunn
Oh my goodness, I just saw it. I would separate the variables into
1/(1+y) . dy = x . dx

and then integrate each side to get
ln (1+y) = x^2/2 + c

Thank you for your help! By the way, how did you format the equations so it looks nicer? :smile:


Yep, well done. It's using LaTex to write the equations. There's a page on TSR showing how to write in LaTeX if you want to use it.
Reply 4
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dyuunn
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Original post by NeverLucky
Yep, well done. It's using LaTex to write the equations. There's a page on TSR showing how to write in LaTeX if you want to use it.

Awesome! Thank you once again.

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