anonymous
  • anonymous
Solve the differential equation by separation of variables ylnx(dx/dy)=((y+1)/x)^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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dape
  • dape
Seperation of variables means you get the x's and dx on one side and y's and dy on the other side. So it should look like \[ f(x)dx=g(y)dy \] Where \(f(x)\) is something involving x's (no y's!) and \(g(y)\) is something involving y's.
dape
  • dape
When you have done this, you can integrate both sides and then solve for y, if you can, to get y as a function of x. This is the solution (don't forget integration constants).
anonymous
  • anonymous
I understand the concept but when I actually try to solve it, I get stuck.

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dape
  • dape
How far did you get?
anonymous
  • anonymous
xylnx(dx)=(y+1)^2 dy and I'm not even sure if that is correct
dape
  • dape
You need to divide by y also, did the differential equation have \(x\) or \(x^2\) in the denominator on the right hand side? If it was \(x^2\) you need another \(x\) on the left hand side.
anonymous
  • anonymous
ok so then I get x^2(lnx)dx=((y+1)^2)/y dy after that I don't know where to go from there since I'm not sure how to integrate each side
dape
  • dape
You will have to do partial integration or integration by parts. This is a skill you will need to master when solving differential equations, I recommend watching through http://youtu.be/ouYZiIh8Ctc if you need to get repetition on the method or http://youtu.be/LJqNdG6Y2cM which is an example to jog your memory, or to watch after you watch the first one.
dape
  • dape
I can check your work on the differential equation later if you want to.
anonymous
  • anonymous
ok thank you very much that actually makes sense know, I had just forgotten about that technique!!
dape
  • dape
For the right hand side you will need to do a substitution to get it into a more familiar form. I would recommend trying something like u=y+1.
zepdrix
  • zepdrix
Hmm I would expand out the numerator on the right side and then divide y out of each term. :O maybe that's just me though.
dape
  • dape
Yeah, you're right, that's way better.

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