For x>1 , if (2 x)^ 2 y =4 e ^ 2 x-2 y , then (1+ _e 2 x )^2 d y d x is equal to

Step-by-step solution

(2 x)^ 2 y =4 e ^ 2 x-2 y Taking ' _ e ' on both sides, we get 2 y _ e (2 x)= _ e 4+(2 x-2 y) _ e e y _ e (2 x)= _ e 2+x-y Differentiating w.r.t. x , we get array ll & [ _ e 2 x ] d y ~d x + 2 y 2 x =0+1- d y ~d x & [1+ _ e 2 x ] d y ~d x =1- y x & Now, (i) y= _ e 2+x 1+ _ e 2 x (ii) & ( ii) (1+ _ e 2 x ) d y ~d x = x _ e 2 x- _ e 2 x (1+ _e 2 x ) . & (1+ _ e 2 x )^2 d y ~d x = x _ e 2 x- _ e 2 x array