Proof Validity: |\frac {dy}{dx}| +|y| + 1 = 0

[zeronem]

This seems like a very easy problem, but I just wanted to know if my proof is valid for it. It is very simple,

Show that the differential equation $$|\frac {dy}{dx}| +|y| + 1 = 0$$ has no solutions.

Well simply this, $$|\frac {dy}{dx}| + |y| = -1$$

The sum of Two Absolute values can never be a negative. Therefore there is no solution for the equation

$$|\frac {dy}{dx}| +|y| + 1 = 0$$

Is this valid? Or do I need more precise wording?

 

[TenaliRaman]

looks good to me! (unless i am overseeing something).

 

[HallsofIvy]

Yes, that's perfectly valid. You could also note that
$$|\frac {dy}{dx}| +|y| + 1$$ cannot be less than 1 and so can never be equal to 0. Although it is not necessary to state it explicitely you should be aware that you are really talking about the value for each x.