Have to find three ways of solving (only have one successful)

  • Thread starter Mabbott608
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In summary, the conversation is about solving the equation x*y'' - y' = 3x^2 using different methods. The speaker has already used the Cauchy-Euler method, but is now trying to use linear differential equations and power series. However, they are having some difficulties and are asking if they are on the right track and which method they should use. Another person suggests making a substitution and finding an integrating factor.
  • #1
Mabbott608
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Homework Statement



x*y'' - y' = 3x^2


The Attempt at a Solution



so far i have used cauch-euler and solved it. i was trying to use linear de and power series to solve, but with little success. Am i on the right track? If not, which method should i be using to find the solution?
 
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  • #2
Mabbott608 said:

Homework Statement



x*y'' - y' = 3x^2


The Attempt at a Solution



so far i have used cauch-euler and solved it. i was trying to use linear de and power series to solve, but with little success. Am i on the right track? If not, which method should i be using to find the solution?

I don't recall the Cauchy-Euler method is, so if that worked for you, great. Power series should work, so if you're having problems, show us what you've done.

You can also make the substitutiion u = y', u' = y'' to make the equation first order, and find an integrating factor. Once you have found u, integrate to get y.
 

What are some common methods for problem-solving?

Some common methods for problem-solving include trial and error, brainstorming, and using a systematic approach.

How can I come up with multiple solutions for a problem?

One way to come up with multiple solutions is to approach the problem from different angles and perspectives. You can also try collaborating with others and gathering their ideas.

What is the benefit of having multiple solutions for a problem?

Having multiple solutions allows for a more comprehensive evaluation of the problem and can lead to a more effective solution. It also allows for flexibility and the ability to adapt if one solution does not work.

How do I determine which solution is the most successful?

The most successful solution can be determined by evaluating the effectiveness, efficiency, and feasibility of each solution. Consider the potential outcomes and consequences of each solution and choose the one that best meets the criteria for success.

What should I do if I only have one successful solution?

If you only have one successful solution, it is important to thoroughly test and evaluate it to ensure its effectiveness. You can also try to think of potential variations or improvements to the solution to make it even more successful.

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