This is Differential equation NEED to be DONE with Maple pro

This is Differential equation,

NEED to be DONE with Maple program.

For all of these, you are going to have to open up Maple Help and type in examples, DEplotSystems. Here you are going to see several interactive ode systems that will help you for this project. An ode system is one which you have more than one ode that is involved in a mathematical model (just like a system of equations you have seen in algebra). Many mathematical models require them because there is usually more than one quantity involved in a process that must all be considered. We do not know how to solve these yet but will use maple to help us. Open up the metastasis of a tumor. Replace the beta parameters with the following: beta_1 = 0.2, Beta_2 = 0.3, beta_3 = 0.5 and beta_1 = 0.2, beta-2 = 0.7, beta_3 = 0.2 and run the commands already there. Explain the results of the depot with real life situation for each set of parameters. Also, use solve to solve this system in terms of constants. Explain what you notice about the exponents in the solution and the values of beta. Now open up the Lotka-Volterra system for prey and predator relationships. What I want you to do is read it over so you know what all the parameters do. Then I want you to look at the plot of the solution. What you will see is points that orbit. What it actually is a is numerical approximations to the data for x and y that solves the system. You will see how they range for x and y values. What I would like you to do is select an appropriate set of parameters to show an example of when a large prey and a small predator population results. Then I want you to do the same for the reverse. You must understand the parameters as well as the ode system.

Solution

Ans-

A plot can also be defined in the discrete or parametric forms. The discrete form is used to plot a set of points with given coordinates. A discrete plot is defined by a list starting with the keyword discrete, followed by one or two lists of values. If two lists are given, they must have the same length; the first list will be interpreted as the x coordinates of the points to be plotted and the second list as the y coordinates. If only one list is given after the discrete keyword, each element on the list could also be a list with two values that correspond to the x and y coordinates of a point, or it could be a sequence of numerical values which will be plotted at consecutive integer values (1,2,3,...) on the x axis.

A parametric plot is defined by a list starting with the keyword parametric, followed by two expressions or function names and a range for the parameter. The range for the parameter must be a list with the name of the parameter followed by its minimum and maximum values: [param,min, max]. The plot will show the path traced out by the point with coordinates given by the two expressions or functions, as param increases from min to max.

A range for the vertical axis is an optional argument with the form: [y, min, max] (the keyword y is always used for the vertical axis). If that option is used, the plot will show that exact vertical range, independently of the values reached by the plot. If the vertical range is not specified, it will be set up according to the minimum and maximum values of the second coordinate of the plot points.

All other options should also be lists, starting with a keyword and followed by one or more values. See plot_options.

If there are several plots to be plotted, a legend will be written to identity each of the expressions. The labels that should be used in that legend can be given with the option legend. If that option is not used, Maxima will create labels from the expressions or function names.