For the differential equation y"+ 16/ +64y = sin(6z) Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is (D+8)- List the complementary functions -8x -8x „re A Part 2: Find the particular solution To solve the non-homogeneous differential equation, we look for functions annihilated by the differential operator (a multiple of the differential operator from above) &r re Therefore the particular solution must be made up of the functions sin (6x). cos( 6x) Substituting these into the differential equation, we find the particular solution is 2500 sin (6x) – cos (6x) 625

Q: the equation ariables x and y and

A:

Q: The deferential of point functions are exact differentials. Select one: True False

A: True

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A: Let say we have two functions f(x) & g(x)Now combine the function f(g(x))Hence, the derivative…

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Q: Problem 9: Suppose A is a 5 x 3 matrix and there exists a 3 x 5 matrix C such that CA = I3. Suppose…

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A: DIFFERENCE BETWEEN INFERENTIAL AND DIFFERENTIAL CALCULUS:…

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A: To find: Method can be used instead of newton method when we do not want to find a derivative.

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Q: can we calculate the derivative of a matrix and the nth root of a matrix ?

A: Yes, derivative of a matrix and the nth root of a matrix both can be calculated.

Q: Is this statement true explain why, if false explain why if x² te=10, then y'= -2x

A: find dy/dx

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A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.