- #1
John777
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In a differential equation in doing a substitution such as z=dy/dx can I do the following:zdx=dy
Integrate both sides
y=zx
Integrate both sides
y=zx
Please verfiy this differential substitution is mathamatically legal
- Thread starter John777
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In summary, when doing a substitution such as z=dy/dx in a differential equation, you can integrate both sides to solve for y. However, this assumes that z is constant, which may not always be the case.
- #2
cepheid
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John777 said:
You can probably get away with doing this, yes.
John777 said:
Ah, but integrate both sides with respect to what?
John777 said:
In taking this step, you have implicitly assumed that z is constant (i.e. that it does not depend on x). Since z = dy/dx, that's not going to be true in general, is it?
Related to Please verfiy this differential substitution is mathamatically legal
1. What is a differential substitution?
A differential substitution is a mathematical technique used to solve integrals that involve a variable in the exponent. It involves substituting a new variable for the original variable and using the chain rule to rewrite the integral in terms of the new variable.
2. Why is it important to verify the mathematical legality of a differential substitution?
Verifying the mathematical legality of a differential substitution is important to ensure that the substitution is valid and does not produce incorrect results. It also helps to avoid errors and inconsistencies in the solution.
3. How do you verify if a differential substitution is mathematically legal?
To verify if a differential substitution is mathematically legal, you need to check if the substituted variable and the original variable have the same domain and range, and if the integral can be rewritten in terms of the substituted variable using the chain rule.
4. What happens if a differential substitution is not mathematically legal?
If a differential substitution is not mathematically legal, it means that the substitution is not valid and will not produce the correct solution. This could lead to errors in calculations and incorrect results.
5. Are there any common mistakes to avoid when using a differential substitution?
Yes, there are some common mistakes to avoid when using a differential substitution. These include incorrectly choosing the substitution variable, not applying the chain rule correctly, and forgetting to account for the differential in the integral.
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