Solve the differential equation `(dy)/(dx)+ycotx=2cosx ,` given that `y=0,` when `x=pi/2dot`

Explanation

Comparing the given equation with first order differential equation,

`dy/dx+Py = Q(x)`, we get,
`P = cotx and Q(x) = 2cosx`

So, Integrating factor `(I.F) = e^(intcotxdx)`

`I.F.= e^(ln|sinx|) = sinx`

we know, solution of differential equation,

`y(I.F.) = intQ(I.F.)dx`

`:.`Our solution will be,

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