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DiffEQ: Determining the largest interval of a solution

  • Thread starter Kaylee!
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  • #1
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The question is to determine the solution to the following 1st order linear DE, along with the largest interval the solution is valid on:

[tex] cosx \frac{dy}{dx} + (sinx)y=1 [/tex]



Rewriting it shows it to be linear:
[tex]\frac{dy}{dx} + (tanx)y = secx[/tex]

The intergrating factor is: [tex]e^{\int{tanx dx}} = e^{-ln|cosx|} = secx[/tex]

Multiplying both sides of the DE by the integrating factor, and rewriting the LHS as a derivative of the product of the integrating factor and y:
[tex]\frac{d}{dx}[(secx)y]= sex^{2}x[/tex]

(secx)y = tanx+c

y = sinx + c(cosx)

------------------

Now how do I determine the interval?
 

Answers and Replies

  • #2
5
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I'm multiplying both sides of the equation by secx, which has a domain of (-pi/2, pi/2), so that's the interval. Is this reasoning correct?
 

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