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question about ordinary differential equations


heikediguoren
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I'm doing an exercise that gives me a list of equations and asks me to identify which ones are ordinary differential equations (hereafter DE).

 

The solutions in the back of the book say that

 

(1) y'' + (2/x)y' + e^(-y) = 0

 

is a DE, but

 

(2) y''' - (1/(x^(1/2)))(y^(3/2)) = 0

 

is not.

 

I don't understand the difference between these two equations. Both contain only an independent variable x, a function y(x), and that function's derivatives. So why is (1) a DE but not (2)? Is my textbook's solution wrong?

 

I can't ask my teacher because I'm not in a class; I just wanted to learn about differential equations so I got a book.

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