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  • Let x^k + y^k = a^k where a , k > 0 and ( dy/dx ) + (y/x)^1/3 =0 then k is

Let x^k + y^k = a^k where a , k > 0 and ( dy/dx ) + (y/x)^1/3 =0 then k is

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Solution: 

x^k + y^k = a^k

diffrentiate w.r.t x of both side we get 

k x^(k -1) + ky^(k -1)( dy/dx) = 0 

⇒   ( dy/dx) = -(x/y)^k -1

⇒  dy/dx + (y/x)^1 - k =0

⇒  ( 1 - k ) = 1/3

⇒   k =2/3 Ans

Posted by

Deependra Verma

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