Differentiate y=xx...∞
y=xx..∞
y=xy
lny=ylnx
Differentiating wrt x
⇒y′y=yx+y′lnx
y′[1−ylnx]=y2x
The differential equation corresponding to primitive y=edx is
or
The elimination of the arbitrary constant m from the equation y=emx gives the differential equation
[MP PET 1995, 2000; Pb. CET 2000]