- #1

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[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)

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Now how do I determine the interval?