anonymous
  • anonymous
How do I solve the differential equation x^2+(x^3+8)y'=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Can I divide each term by 1/dy to separate?
anonymous
  • anonymous
This is in the form m+ny'=0
anonymous
  • anonymous
see if its exact

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anonymous
  • anonymous
do the partial with respect to y for the m and then do the partial with respect to x in the n portion
anonymous
  • anonymous
Start by isolating y' .. then integrate both sides
anonymous
  • anonymous
if they are equal then it is exact
anonymous
  • anonymous
But to isolate y' I would need to divide each term by y' correct?
anonymous
  • anonymous
wait...is this cal 1 or differential equations and linear algebra
anonymous
  • anonymous
Calc II differential equations
anonymous
  • anonymous
http://1337.is/~gaulzi/tex2png/view.php?png=201103312034348813.png would look like this isolated
anonymous
  • anonymous
Well you can try implicit differentiation.
anonymous
  • anonymous
take the derivative of the first term with respect to x
anonymous
  • anonymous
kristin wouldn't it be -x^2?
anonymous
  • anonymous
sorry yes, thats correct, minor typo :)
anonymous
  • anonymous
Ok no problem. Thanks
anonymous
  • anonymous
I can toss up for you the answer if you want :)
anonymous
  • anonymous
y' is dy/dx correct? If i were to rewrite it
anonymous
  • anonymous
yeah
anonymous
  • anonymous
Ok so if I were to solve y'+y=10 would I just replace y' with dy/dx and then move it all around?
anonymous
  • anonymous
I'm trying to figure out the steps
anonymous
  • anonymous
it can be done by the separable variables method
anonymous
  • anonymous
after some modification you can get dy=-x^2/(x^3+8) dx just integrate both sides
anonymous
  • anonymous
http://1337.is/~gaulzi/tex2png/view.php?png=201103312042017465.png these are the two answers you can get.. depends if you like to use ln or log
anonymous
  • anonymous
I know the answer I'm trying to figure out the steps, could you show me the steps kristin? Plz.
anonymous
  • anonymous
I can show it to you
anonymous
  • anonymous
did you integrate like she said?
anonymous
  • anonymous
I know I need to integrate each piece, I just need to know how to get each piece by itself
anonymous
  • anonymous
do a u substitution
anonymous
  • anonymous
u=x^3+8 du=3xdu
anonymous
  • anonymous
du=3x^2 sorry
anonymous
  • anonymous
you should get: integral( -1/3(1/u) dx
anonymous
  • anonymous
just take u=x^3+8 --> du=3x^2dx substitute in the integral you will get \[y=-1/3\int\limits_{}^{}(1/u)du=-1/3\ln \left| u \right|\]
anonymous
  • anonymous
now just substitute for u=x^3+8 \[y=-1/3\ln \left| x^3+8 \right|+c\]
anonymous
  • anonymous
Oh right I got that. Thanks
anonymous
  • anonymous
np

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