Determine if the equation is a differential equation.
f (2)(x) + f (x) = 7x
Answer
Yes
x2 + f 2(x) = 0
No, because f 2(x) means the square of f, not the second derivative of f.
x2 + y2 = 4xy
No, because there are no derivatives in this equation.
y + y2 + y3 = x
y' + 2y'' = 3 – x
Determine the order of the differential equation.
This differential equation has order 2:
y" + y' – y = 0
The highest derivative we have is a second order one, so the order is two.
f '(x) = x2 + 3x + 5
This differential equation has order 1:
f (x) – f 3(x) + f (2) = 7x
f (x) - f 3(x) + f (2) = 7x
The order is 2.
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