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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