y=log{e^(a)*((a-2)/(1+a))^((3)/(4))}

If y = log {:{(e^x((x-2)/(x+2))^3/4):}} , show that dy/dx = (x^2 -1)/(x^2-4)

Let y(x) is the solution of differential equation (dy)/(dx)+y=x log x and 2y(2)=log_(e)4-1 Then y(e) is equal to (A) (e^(2))/(2) (B) (e)/(2)(C)(e)/(4)(D)(e^(2))/(4)

Let y=y(x) be the solution of the differential equation,x((dy)/(dx))+y=x log_(e)x,(x>1) if 2y(2)=log_(e)4-1, then y(e) is equal to: (a)-((e)/(2))(b)-((e^(2))/(2))(c)(e)/(4)(d)(e^(2))/(4)

2[1+((log_(e)a)^(2))/(2!)+((log_(e)a)^(4))/(4!)+....] =

(1)/(log_(2) e) + (1)/(log_(2)e^(2)) + (1)/(log_(2) e^(4)) + .... =

1+2(log_(e)a)+(2^(2))/(2!)(log_(e)a)^(2)+(2^(3))/(3!)(log_(e)a)^(3)+....=

If y=tan^(-1)[(log(e//x^(3)))/(log(ex^(3)))]+tan^(-1)[(log(e^(4)x^(3)))/(log(e//x^(12)))]," then "(d^(2)y)/(dx^(2))=