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Math Help - differential equation with trig

  1. #1
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    differential equation with trig

    \tan (\theta )\frac{{dr}}<br />
{{d\theta }} + r = {\sin ^2}(\theta ),\frac{\pi }<br />
{4} < \theta  < \frac{\pi }<br />
{2}<br />

    not sure where to begin...
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  2. #2
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    Quote Originally Posted by genlovesmusic09 View Post
    \tan (\theta )\frac{{dr}}<br />
{{d\theta }} + r = {\sin ^2}(\theta ),\frac{\pi }<br />
{4} < \theta < \frac{\pi }<br />
{2}<br />

    not sure where to begin...

    \frac{dr}{d\theta}=\frac{\sin^2\theta-r}{\tan\theta} =\sin\theta\cos\theta-r\frac{\cos\theta}{\sin\theta}\Longrightarrow r\theta=\int \sin\theta\cos\theta\,d\theta-r\int \frac{\cos\theta}{\sin\theta}\,d\theta ...now end the exercise.

    Tonio
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