What's the difference between these two D.E?

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In summary, the two given examples are both differential equations that use the Frobenius method. However, they use different methods to solve them. The first example uses the method of variation of parameters, while the second one uses the assumption that y2=cy1 and differentiates that and substitutes it into the original equation. It is important to note that these are not actually considered Frobenius methods, as Frobenius refers to the use of a power series solution for differential equations.
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asdf1
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1. x(x-1)y``+(3x-1)y`+y=0
2. (x^2 -x)y``-xy`+y=0
those are 2 examples of the frobenius method, but i don't understand why those 2 use completely different methods to solve...
 
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What methods were used to solve each of them?
 
  • #3
the first used the method of variation of parameters, and the second one
supposed that y2=cy1 and differentiated that and subsituted y2``, y` and y into the original equation...
 
  • #4
Firstly, can you stop calling DEs frobenius: they are not. Frobenius refers to the use of a power series solution for DEs, there are different ways to work out what that power series is.
 

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