Verify a function is a solution.

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In summary, the conversation discusses verifying that a given solution is valid for a first-order differential equation. The method suggested is to eliminate the constant and then plug in the function and its derivative to show equality with the DE. This method is considered effective and there may be alternative approaches to proving the validity of the solution.
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Verify that x^2 + y^2 = cy is a solution of dy/dx = (2xy)/(x^2-y^2) where c is a constant.

I don't know how i should start this problem. I've done a couple DE questions but nothing like this.. Thanks
 
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One trick I learned (from Jester) when doing these problems is to eliminate the constant $c$, whenever possible, for first-order. To do that, simply solve for the constant and then take the necessary derivative. Your goal here is to plug the function and its derivative into the DE and show that you get equality.
 
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FAQ: Verify a function is a solution.

What is the purpose of verifying a function as a solution?

Verifying a function as a solution is important in science because it allows us to determine if the function correctly describes a relationship between variables. This helps to ensure the accuracy and reliability of our data and conclusions.

How do you verify a function as a solution?

To verify a function as a solution, you need to substitute the values of the independent variable into the function and calculate the corresponding values of the dependent variable. Then, compare these calculated values to the actual data points to see if they match.

What are the potential errors in verifying a function as a solution?

One potential error in verifying a function as a solution is human error, such as making a mistake in calculating or recording data. Another error could be using an incorrect function or not considering all relevant variables in the relationship.

Can a function be a solution to more than one set of data?

Yes, a function can be a solution to multiple sets of data if it accurately describes the relationship between the variables in each set.

How does verifying a function as a solution contribute to the scientific method?

Verifying a function as a solution is an essential step in the scientific method because it allows us to test our hypotheses and make accurate conclusions based on empirical evidence. It also helps to ensure the validity and reproducibility of scientific experiments and studies.

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