Question

The maximum number of arbitrary constants is equal to
a. Number of derivatives in the differential equation
b. Degree of differential equation
c. Order of differential equation
e. None of the above

I don't understand this, but my guess it's letter A. Please help.

Answer 1

C

y" + (y')^2 + y^3 = f(x)
is a 2nd order equation. You have to integrate twice to get y, and that introduces two constants.

It is a 3rd-degree equation, because of y^3

Doesn't matter how many derivatives are present. Just their order. Better review DE's. Here is a place to start:

http://www3.ul.ie/cemtl/pdf%20files/bm2/DegreeOrder.pdf