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

[asdf1]

for
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...

 

[Tide]

What methods were used to solve each of them?

 

[asdf1]

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...

 

[matt grime]

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.