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I had a question, I solved a problem very similar to this one but it has 2 real soltions which took the form of:

y (x) = Ae^rx + Be^(rx)

But now i have repeated roots:

y(x) = e^(rx)*(A + Bx);

HEre is the problem:

Find y as a function of x if

x^2 y'' - 11 x y' + 36 y = 0,

y(1) = -2, y'(1) = -3.

y=

Ivey told me i could should change e^(rx) to just x^r in my last problem which worked great!

Now if i have a repeated root case how would I do this? would it be:

y(x) = x^r(A+Bx)?

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# Can i apply the same technique as I did with real solutions? D.E. 2nd order

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