anonymous
  • anonymous
solve the DE using exact method: [sin(xy) + xycos(xy)]dx + [1 + x^2cos(xy)]dy=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
i know its exact I am getting stuck on doing the integral of Mdx
anonymous
  • anonymous
Integration by parts on the xycos(xy) doesnt work?
anonymous
  • anonymous
it works but then i keep ending up having to do it several times over and over so something is wrong

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anonymous
  • anonymous
k
anonymous
  • anonymous
k so for the integration by parts i got xsin(xy) + cos(xy)/y
anonymous
  • anonymous
take the integral of [1 + x^2cos(xy)} instead
anonymous
  • anonymous
thats not what my rule says to do so i cant
anonymous
  • anonymous
believe me you can
anonymous
  • anonymous
i know you can but my professor wont allow it
anonymous
  • anonymous
i didnt get the same answer for the integration by parts
anonymous
  • anonymous
it would be the integral of x/ysin(xy)dx so i took out of the 1/y since its considered a constant so your left with xsin(xy)dx which requires IP again :(
anonymous
  • anonymous
take the integral of [1 + x^2cos(xy) with respect to y then take the ppartial with respect to t - do you see what I am saying -- you do it the same but opposite
anonymous
  • anonymous
then i would be using the h(y) as h(x) since i am using the complete opposite formula now
anonymous
  • anonymous
i will figure it out that way...thanks
anonymous
  • anonymous
you will get \[y+ xsin(xy) \] this is the interal of [1 + x^2cos(xy) with respect to y then take the partial with respect to x
anonymous
  • anonymous
yeh exactly what i got....thankss
anonymous
  • anonymous
dont forget your constant \[\phi(x)\]
anonymous
  • anonymous
yupp
anonymous
  • anonymous
\[\phi(x)=0\] so the solution is y+xsin(xy)=c
anonymous
  • anonymous
yup i got that...thanks so much
anonymous
  • anonymous
that is the good thing about exact form if you cant take the intergral of M try the integral of N
anonymous
  • anonymous
yeh i am glad i know that now....only one more problem to go with this DE stuff and im done
anonymous
  • anonymous
where do you go to school
anonymous
  • anonymous
college of saint elizabeth....small womans college in nj

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