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For the differential equation, find a ...

For the differential equation, find a particular solution satisfying the given condition: `(dy)/(dx)+2ytanx=sinx ; y=0` when `x=pi/3`

Text Solution

Verified by Experts

Comparing the given equation with first order differential equation,
`dy/dx+Py = Q(x)`, we get, `P = 2tanx and Q(x) = sinx`
So, Integrating factor `(I.F) = e^(int2tanxdx)`
`I.F.= e^(2ln secx) = e^(ln sec^2x) = sec^2x`
We know, solution of differential equation,
`y(I.F.) = intQ(I.F.)dx`
`:.`Our solution will be,
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