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

  • Thread starter zeronem
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In summary, the differential equation |\frac {dy}{dx}| +|y| + 1 = 0 has no solutions because the sum of two absolute values can never be negative. This proof is valid as it shows that the equation |\frac {dy}{dx}| +|y| + 1 cannot be less than 1 and therefore can never be equal to 0. It is also important to note that this applies for all values of x.
  • #1
zeronem
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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 [tex] |\frac {dy}{dx}| +|y| + 1 = 0 [/tex] has no solutions.

Well simply this, [tex] |\frac {dy}{dx}| + |y| = -1 [/tex]

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

[tex] |\frac {dy}{dx}| +|y| + 1 = 0 [/tex]

Is this valid? Or do I need more precise wording?
 
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  • #2
looks good to me! (unless i am overseeing something).
 
  • #3
Yes, that's perfectly valid. You could also note that
[tex] |\frac {dy}{dx}| +|y| + 1 [/tex] 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.
 

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

How do you determine the validity of a proof?

The validity of a proof is determined by carefully examining the logical steps and assumptions used to arrive at the conclusion. This includes checking for any errors in reasoning, ensuring that all statements are supported by evidence, and verifying that the proof follows the rules of logic.

What makes a proof valid?

A proof is considered valid if it follows a logical sequence of steps that lead to the desired conclusion, without any errors or assumptions that are not supported by evidence. Additionally, a valid proof must also adhere to the rules of logic and mathematical principles.

How do you know when a proof is invalid?

An invalid proof is one that contains logical errors, incorrect assumptions, or steps that do not follow the rules of logic. These errors can often be identified by examining the reasoning behind each step and checking for any inconsistencies or unsupported claims.

Can a proof be both valid and incorrect?

No, a proof cannot be both valid and incorrect. A valid proof follows a logical sequence of steps that lead to the correct conclusion, while an incorrect proof contains errors or assumptions that do not align with the evidence or rules of logic.

How can you improve the validity of a proof?

To improve the validity of a proof, it is important to carefully review each step and ensure that they are all supported by evidence and follow the rules of logic. Additionally, seeking feedback and double-checking calculations can also help to identify and correct any errors in the proof.

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