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

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

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=e^(log_(e)(1+e^(log_(e)x))) then (dy)/(dx)=

Let y= y(x) be solution of the differential equation log_(e)((dy)/(dx)) =3x+4y , with y(0)=0. If y(-(2)/(3)log_(e)2)=alpha log_(e)2 , then the value of alpha is equal to

The solution of the differential equation (dy)/(dx) + (y)/(x log_(e)x)=(1)/(x) under the condition y=1 when x=e is

Solution of the equation x (dy)/(dx) = y log y is

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