Classifying differential equations

[kcoe05]

Classify each of the following differential equations as exact or non-exact and justify why.

dy/dx= ycosx / (1+sinx)


dy/dx = -x^2 (3y^2 + 1) / y(2x^3 + 1)


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


(x+y) + (4y + ln x) dy/dx = 0



Thank you for any help you can give me.

 

[Deleted member 4993]

Classify each of the following differential equations as exact or non-exact and justify why.

dy/dx= ycosx / (1+sinx)


dy/dx = -x^2 (3y^2 + 1) / y(2x^3 + 1)


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


(x+y) + (4y + ln x) dy/dx = 0



Thank you for any help you can give me.

What is the definition of "exact differential equations"? What are their properties?

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