D.E. Cauchy-Euler Method: Have I made any mistakes

Thread starter Jeff12341234
Start date Mar 18, 2013
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In summary, the D.E. Cauchy-Euler method is a technique used to solve linear differential equations with constant coefficients by converting the equation into a power series and solving for the coefficients. It is commonly used in engineering, physics, and other scientific fields and can be checked for mistakes by comparing the solution to the original equation and double-checking calculations. Common mistakes include errors in determining coefficients and incorrect substitution of the power series.

Mar 18, 2013

Jeff12341234

This problem seems suspiciously simple. Have I made any mistakes?

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Mar 18, 2013

Mark44

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Insights Author

Presumably, you checked your work. Since there are no initial conditions, it is not possible to solve for the constants.

BTW, please shrink your posted images a little, to no more than 900 x 600 pixels.

1. What is D.E. Cauchy-Euler method?

The D.E. Cauchy-Euler method, also known as the power series method, is a technique used to solve linear differential equations with constant coefficients. It involves converting the differential equation into a power series and then solving for the coefficients.

2. How does the D.E. Cauchy-Euler method work?

The D.E. Cauchy-Euler method works by converting the given differential equation into a power series of the form y = ∑(n=0 to ∞) a_n x^n. The coefficients a_n can then be determined by substituting the power series into the differential equation and solving for each term.

3. What are the applications of the D.E. Cauchy-Euler method?

The D.E. Cauchy-Euler method is commonly used in engineering, physics, and other scientific fields to solve differential equations that arise in various problems. It is also used in the study of vibrations, mechanics, and other areas of mathematics.

4. What are some common mistakes made when using the D.E. Cauchy-Euler method?

Some common mistakes made when using the D.E. Cauchy-Euler method include errors in determining the coefficients of the power series, incorrect substitution of the power series into the differential equation, and not considering all possible solutions to the equation.

5. How can I check if I have made any mistakes when using the D.E. Cauchy-Euler method?

To check for mistakes when using the D.E. Cauchy-Euler method, you can compare your solution to the original differential equation, substitute the solution back into the equation to see if it satisfies the equation, and double-check your calculations for the coefficients of the power series.