If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo))),` then show that `dy/dx=cosx/(2y-1)`

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#### Solution

`y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo)))`

Let `y=sqrt(sinx+y)`

`y^2=sinx+y `

Differentiat ing w.r.t.x,

`2y.dy/dx=cosx+dy/dx`

`dy/dx=cosx/(2y-1)`

Concept: General and Particular Solutions of a Differential Equation

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