Steps

9.2 Second-order difference equations. Definition A second-order difference equation is an equation. xt+2 = f(t, xt, xt+1), where f is a function of three variables.

Definition 17.1. 1 A first order differential equation is an equation of the form F(t,y,˙y)=0. A solution of a first order differential equation is a function f(t) that makes F(t,f(t),f′(t))=0 for every value of t.

1. Substitute y = uv, and.
2. Factor the parts involving v.
3. Put the v term equal to zero (this gives a differential equation in u and x which can be solved in the next step)
4. Solve using separation of variables to find u.
5. Substitute u back into the equation we got at step 2.
6. Solve that to find v.

Difference equation, mathematical equality involving the differences between successive values of a function of a discrete variable.

more The result of subtracting one number from another. How much one number differs from another. Example: The difference between 8 and 3 is 5.

Difference equations are used in a variety of contexts, such as in economics to model the evolution through time of variables such as gross domestic product, the inflation rate, the exchange rate, etc. They are used in modeling such time series because values of these variables are only measured at discrete intervals.

Differential Operator L(D) In other words, the operator L(D) is an algebraic polynomial, in which the differential operator D plays the role of a variable. Let us consider some properties of the operator L(D). The operator L(D) is linear: L(D)[C1y1(x)+C2y2(x)]=C1L(D)y1(x)+C2L(D)y2(x).

You can actually use the derivative of ln ⁡ ( x ) /ln(x) ln(x)natural log, left parenthesis, x, right parenthesis (along with the constant multiple rule) to obtain the general derivative of log ⁡ b ( x ) /log_b(x) logb(x)log, start base, b, end base, left parenthesis, x, right parenthesis.

Use the half angle formula, sin^2(x) = 1/2*(1 – cos(2x)) and substitute into the integral so it becomes 1/2 times the integral of (1 – cos(2x)) dx.

2sinx is twice the trigonometric function sinx whereas 2x in sin2x represents angle. Sin(2x) is a function with a different “argument.” For example, if x=90-degrees, then sin(x) = 1, but sin(2x) =0. Of course, 2sin(x) would equal 2.

= sin A cos B + cos A sin B.

Compendium. that’s correct, sin(x)^2=(sin(x))^2, if you are using a graphing calculator. On most scientific calculators, you enter x first, push the sin button, then hit the squared button.