Do differential equations have to contain unknown functions? Can only its derivative be called a differential equation?

Do differential equations have to contain unknown functions? Can only its derivative be called a differential equation?

Differential equations must not contain unknown functions. Only the derivative of a function is a differential equation

The equation in which the unknown function and its derivatives are of one order becomes a linear differential equation

Once means that the unknowns are all one-time terms, and there are no multiple terms such as square terms and cubic terms

Single choice 9. If the unknown function and its derivatives of ordinary differential equation are of primary form, the equation is called () A: First order equation B: Second order equation C: Homogeneous equation D: Linear equation

D
The first order and the second order refer to the highest order of the derivative of the unknown function
Homogeneous means that the order and sum of derivatives of unknown functions in each term are the same
The equation with the highest order of linear guidance number is one

Find the derivative expression of independent variable of complex function: F (x) = [M (1-x) ^ P + n] ^ (1 / P). P, m and N are constant

f'(x)=1/p *[m(1-x)^p+n]^(1-1/p) *m*(-p)*(1-x)^(p-1)=-m*[m(1-x)^p+n]^(1-1/p) *(1-x)^(p-1)

It is known that the function y = x + A / X has the following properties: if the constant a > 0, the function is a subtractive function on (0, √ a] and an increasing function on [√ a, + ∞) (1) If the function y = x + (2 ^ b) / X (x > 0) is a subtractive function on (0,4) and an increasing function on [4, + ∞), find the value of B; (2) Let the constant C ∈ [1,4], find the maximum and minimum values of the function f (x) = x + C / X (1 ≤ x ≤ 2); (3) When n is a positive integer, the monotonicity of the function g (x) = x ^ n + C / (x ^ n) (c > 0) is studied and the reason is explained

(1) √ (2 ^ b) = 4B = 4 (2) f (x) = x + C / X is a subtractive function on (0, √ C), √ C ∈ [1,2], so the minimum value is f (√ C) = 2 √ CF (1) = 1 + C f (2) = 2 + C / 2, so when C ∈ [1,2], the maximum value is f (1) = 2 + C / 2, C ∈ [2,4]. When n is a positive integer, x ^ n monotonically recurs on r

It is known that the function f (x) = x / ax + B (a, B is a constant, and a is not equal to 0) satisfies that f (2) = 1, f (x) = x has only a unique real number solution, and the analytical formula of function y = f (x) is obtained There are two answers: 1. One is f (x) = 2x / (x + 2), which I know 2. The other is f (x) = 1 (when ax Λ 2 + (B-1) x = 0 has unequal real roots, and one of them is the additive root of the equation) Just tell me number two,

F (x) = x, i.e. X / (AX + b) = x
ax ²+ (B-1) x = 0, the solution is x = 0 or (1-B) / A
∵ f (x) = x has only a unique real number solution
Two are either equal or one of them is meaningless
If x = (1-B) / A, the denominator is always 1, which is always meaningful
If x = 0 is meaningless, when x = 0, the denominator must also be equal to zero. At this time, B = 0, and a = 1 is obtained from F (2) = 1