distinguish between the characteristics of first and second order difference equations.Give examples of economic problem that are solved with the help of each category of such equations.
Answers
Answer:
Differential equation (D.E.) is an equation which involves in it the derivatives (dy/dx) of a function y = f(x) . For example, dy/dx + py = q , while a difference equation (d.e.) involves differences of terms in a sequence and it can be expressed in terms of shift operator E or forward difference operator Δ . For example;
U(n + 2) - U(n +1) - U(n) = 0 … .. . . (1) and it can be written as;
[E² - E - 1]U(n) = 0, n= 0, 1, 2, … ..n …. .
Difference equations (d.e.)as one given in eq.(1) are very useful in describing the discrete problems involving discrete signals while D. E. are used in anolog system involving continuous signals. In fact a d. e.is a discrete version of a D. E. ; for example the d.e. (1) is a discrete form of the D. E. dy/dx = y .
Explanation:
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Answer: An equation: dy/dx= f(x,y) of two variables x and y with the functions f(x,y) in the xy- plane is a first-order differential equation.
An equation y" + p(x)y = 0, if the functions p(x) and q(x) are constant, with constant coefficient are a second order differential equation.
Explanation:
An equation dy/dx= f(x,y) of two variables x and y with its function f(x,y) defined in the xy- plane on a region. The first derivative dy/dx so that the equation is of the first order, and no higher-order derivatives exist. An equation can also be written as:
y’ = f (x,y) or
(d/dx) y = f (x,y)
The used technique for determining the functions over its domain is if we know the derivatives and the functions in physics and chemistry. The derivations of the product of y and any of its derivatives are not present. Any transcendental functions like logarithmic and trigonometric functions have not existed.
An equation y'' + p(x)y' + q(x)y = 0, called a second order differential equation. The functions p(x) and q(x) are constant with constant coefficients. A variable coefficients if p(x) and q(x) are not constant.
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To know more about the second-order differential equation, click on the link
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