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THE CLO1 was comprised of these 2 major topics:
Module 1: Definitions
1.1. Definition and Classifications of Differential Equations (D.E.) by type
1.2. Solution of a D.E. (General and Particular)
Module 2: Solution of Some 1st Order, 1st Degree D.E.
2.1. Variable Separable
2.2. Exact Equation
2.3 Linear Equation
2.4 Substitution Methods
2.4.1 Homogenous Coefficients
2.4.2. Bernoulli’s Equation
One problem application that was stuck in my mind in this classwork assignment would be item #1 in a solution of a differential equation, the application tackles the verification of a certain solution to a differential equation. I did get the answer saying that the given is not a solution to another given differential equation due to the fact that the answer is not equal to 0.
Module 1: Definitions
In this module, differential equation is defined as an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point. It is mainly used in fields such as engineering, physics, biology, and so on. The primary purpose of the differential equation is the study of solutions that satisfy the equations and the properties of the solutions. I also understand the Classifications of Differential Equations by type which goes like this: differential equation is an ordinary differential equation (ODE) if the unknown function depends on only one independent variable. If the unknown function depends on two or more independent variables, the differential equation is a partial differential equation (PDE).
Another thing that was stated here is the Solution of a D.E. (General and Particular). The basic concept being brought up here would be the concept regarding the difference between the two. To expound, the definition of General Solution is that it is a solution which contains a number of independent constants equal to the order of the differential equation. On the other hand, the definition of Particular Solution is that it is a solution which can be contained from the general solution by solving the specific value of the arbitrary constant present.
Upon learning the basics, I learned that differential equation doesn't only be applied in a short basis but for a longer one since it is applied in such industries like engineering, etc.
It is evident in this topic that I determined the solution of the different types of differential equations.
In addition to module 1, it is reflected in mine the discussion regarding the elimination of arbitrary constant as well as the differential equation. What I learned is that ELIMINATION OF ARBITRARY CONSTANT has its own set of PROPERTIES and these are as follows:
• The order of differential equation is equal to the number of arbitrary constants.
• The differential equation is consistent with the relation.
• The differential equation is free from arbitrary constants
Another thing is regarding the family of curves, it is reflected in mine that FAMILIES OF CURVES refers to the set of curves whose equations are of the same form but which have different values assigned to one or more parameters.
One problem application that was stuck in my mind in this coursework would be item #2, the application tackles about the elimination of the arbitrary constants. What I learned is that top answer the problem, it is important to determine first the number of arbitrary constants so that we know how to eliminate each of them, and after that, we can arrive now to the final answer which I learned to be accurate.
It is evident in this topic that I determined the solution of the different types of differential equations.
Module 2: Solution of Some 1st Order, 1st Degree D.E.
This module introduces the basic concepts, principles and theories of surveying. It includes measurement of distance and errors in measurement.
I learned here the definition of General Solution. A solution which contains a number of independent constants equal to the order of the differential equation. Another thing is about the definition of Particular Solution. A solution which can be contained from the general solution by solving the specific value of the arbitrary constant present. Neaxt thing was the Differential Equation of First Order and First Degree. A differential equation of first order and first degree may be written in the form. M (x,y) dx + N(x,y) dy=0 where M and N are both functions of x and y.
One problem application that was stuck in my mind in this classwork assignment would be item #1 in variable separable differential equations, the application tackles about the solution to an equation. I did get the answer saying that the given is in a form of M dx + N dy = 0 and by following the required format in answering the question, I can easily arrive to the final answer.
It is evident in this topic that I determined the solution of the different types of differential equations.
In addition to module 1, it is reflected in mine the discussion regarding the Homogeneous Functions
Definition: The differential equation M(x, y) dx + N(x, y) dy = 0 is said to be homogeneous when M and N are homogeneous functions of the same degree in x and y.
A function is said to be homogeneous when f(kx, ky) = k^n f(x, y) where n is the degree of the function.
One problem application that was stuck in my mind in this problem set would be item #3, the application tackles about the homogeneous differential equations. What I learned is that to answer the problem, it is important to determine first if the equation is the homogeneous equation and following the required format, we can easily determine that it is the equation and after that, we can arrive now to the final answer by simply following the steps required to answer the problem which I learned to be accurate.
It is evident in this topic that I determined the solution of the different types of differential equations.
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