If `x(dy)/(dx)+2y=log_(e)x` then `[(e^2 y(e)-y(1))/(e^2+1)]=`

If y=e^(log_(e)x)," then "(dy)/(dx)=

IF y = y (x) is the solution of the differential equation, x (dy)/(dx) = y (log_(e) y - log_(e) x + 1) , when y(1) = 2, then y(2) is equal to _______

If y = log_(a) x then (dy )/(dx) at x =e is

If (dy)/(dx)-y log_(e) 2 = 2^(sin x)(cos x -1) log_(e) 2 , then y =

If y=log_(e)x+sinx+e^(x)" then "(dy)/(dx) is

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)

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)

If x(dy)/(dx)=y(log_(e)y-log_(e)x+1) ,then solution of the equation is

If y=tan^(-1){((log)_(e)(e/x^(2)))/((log_(e)(ex^(2)))}+tan^(-1)((3+2(log)_(e)x)/(1-6(log)_(e)x)), then (d^(2)y)/(dx^(2))=(a)2(b)1(c)0(d)-1

If quad y=tan^(-1){(log_(e)((e)/(x^(2))))/(log_(e)(ex^(2)))}+tan^(-1)((3+2log_(e)x)/(1-6log_(e)x)), then (d^(2)y)/(dx^(2))=