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Consider the differential equation

[tex]\cos(y'') + xy' = 0[/tex]

How do you determine the order and degree of such a DE?

One way is to write

[tex]y'' = \cos^{-1}(-xy')[/tex]

and say that the order is 2 degree is 1.

But if I do not use the inverse cosine, and observe that the first member on the left hand side is a power series in [itex]y''[/itex], then the order is still 2, but the degree is not defined. What is the resolution to this problem?

PS--This is not homework.

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# How are order and degree defined for this DE? (cos(y'') + xy' = 0)

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