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Find a particular solution of the diffe...

Find a particular solution of the differential equation `(dx)/(dy)+ycotx=1(x!=0)4xcose c x``(x!=0)`, given that `y = 0`when `x=pi/2`

Text Solution

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Given,
`=>(dy)/(dx)​+ycotx=4xcosec x`
So,IF `=>e^∫(cotxdx)`
`=>sinx`
thus,the general solution is `=>y×sinx=∫4xsinx.cosec xdx`
`=>y×sinx=∫4xdx`(since sinx.cosec x=1)
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