anonymous
  • anonymous
\[xy'+y=y ^{2},y(1)=-1\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
i reached \[2\tanh ^{-1}(1-2y)=\ln x+c\]
anonymous
  • anonymous
any kind soul can guide me?
TuringTest
  • TuringTest
Let me call on people that may be able to answer this: @across @lalaly @JamesJ @ash2326 it's just beyond me, sorry look forward to seeing the solution :)

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More answers

anonymous
  • anonymous
owh kk ty. actually i dont know what is tanh also. i reached the tanh based on the integration table ._. lol
experimentX
  • experimentX
looks like Bernoulli's eqn
experimentX
  • experimentX
http://en.wikipedia.org/wiki/Bernoulli_differential_equation
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=xy%27%2By+%3D+y%5E2%2C+y%281%29+%3D+-1
anonymous
  • anonymous
ou im using separable method. anyway, can explain how \[2\tanh ^{-1}(1-2y)=\ln x+c\]becomes\[\ln(1-y) -\ln y=\ln x+c\] basically its the LHS tat i dont understand
experimentX
  • experimentX
http://upload.wikimedia.org/wikipedia/en/math/8/e/f/8ef979b2cbfb464fd813a557fdc8a4ec.png
anonymous
  • anonymous
ou.. ._. never knew there's such thing. TQ! =)
anonymous
  • anonymous
er, but if z=1-2y, why after becoming ln its 1-y
experimentX
  • experimentX
should be 1/2*2(ln(1+1-2y) - ln(2y)) = ln2(1-y) - ln2y = ln 2 + ln(1-y) - ln 2 - ln y
TuringTest
  • TuringTest
\[\tanh ^{-1}z=\frac12\ln(1+z)-\ln(1-(1-2y))\]\[\tanh ^{-1}z=\frac12[\ln(1+1-2y)-\ln(1-z)]=\ln2+\frac12\ln(1-y)-\frac12\ln y\]yep, experimentX beat me to it again ln2 is a constant which can be absorbed into C is the point...
experimentX
  • experimentX
you missed ln 2 at last .. lol
anonymous
  • anonymous
owh. now i get it... ._. TQVM =)
TuringTest
  • TuringTest
d'oh, I was racing you too much :/ so they just cancel anyway...

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