anonymous
  • anonymous
find all the solutions of y'sinx+ycosx=1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[ y'+y\cot(x) = \csc(x) \]
anonymous
  • anonymous
I think you'd find the homogeneous solution and then the particular one.
anonymous
  • anonymous
|dw:1378625378900:dw|

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anonymous
  • anonymous
it's linear equation so I'd use an integrating factor, I'd start by dividing each term by sin x.
anonymous
  • anonymous
|dw:1378625564693:dw|
anonymous
  • anonymous
Now from here we need ti find the integrating factor. The integrating factor is e to the integral of the coefficient of the y term
anonymous
  • anonymous
|dw:1378625678512:dw|
anonymous
  • anonymous
Sine the y term is multiplied by cot x we need to integrate that, how should we integrate cot x?
anonymous
  • anonymous
I'd start by writing it in terms of sin and cos.
anonymous
  • anonymous
?
inkyvoyd
  • inkyvoyd
the integral of cot x should be memorized - it's something like -ln|sin x|. Cause like, yolo
goformit100
  • goformit100
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