So I've solved a differential equation to the point of having : $$-ke ^{-t} + ke ^{-t} = 0$$

What is the most correct way to describe k? Should I just say "k can be any number" or is there a more sound or mathematically descriptive way to go about this?

Question

So I've solved a differential equation to the point of having : $$-ke ^{-t} + ke ^{-t} = 0$$

What is the most correct way to describe k? Should I just say "k can be any number" or is there  a more sound or mathematically descriptive way to go about this?

sidsiddhartha · Answer

any arbitrary number

anonymous · Answer

The LHS is identically equal to 0, whatever the value of k.  So k cannot be determined at all.

sidsiddhartha · Answer

like Ae^ax+Be^bx
then u can say A,B are any arbitrary numbers or constants

anonymous · Answer

Ok cool, thats what I figured, wanted to make sure I wasn't missing anything or needed to restrict it etc... thanks for the feedback

sidsiddhartha · Answer

^_^