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Solution - If  y=√(sinx+√(sinx+√(sinx+.....∞ ))), then show that dy/dx=cosx/(2y-1) - General and Particular Solutions of a Differential Equation

Question

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

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)`

 

Is there an error in this question or solution?

APPEARS IN

2014-2015 (March)
Question 4.2.2 | 2 marks
Solution for question: If  y=√(sinx+√(sinx+√(sinx+.....∞ ))), then show that dy/dx=cosx/(2y-1) concept: General and Particular Solutions of a Differential Equation. For the courses HSC Arts, HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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