Is this project an undergraduate, graduate, or faculty project?
Undergraduate
Project Type
group
Campus
Daytona Beach
Authors' Class Standing
Jacob Schwamb, Sophomore Edward Whipple, Sophomore
Lead Presenter's Name
Jacob Schwamb
Lead Presenter's College
DB College of Engineering
Faculty Mentor Name
Dr. Jorge Gonzalez
Abstract
The general solution analysis of homogeneous linear equations are any systems of equations in which all constant terms are equal to zero is classified as a homogeneous linear equation. Some key characteristics of homogeneous linear equations are that there are “zero” solutions, where every system has at least a single solution where all variables are zero, also all solutions to any homogenous linear equation is linearly independent, along with having preserved homogeneity, where if any variable (x) may be added to the system, then any scalar multiple of the variable is also a solution. The General solution of any homogeneous linear differential equation is formed by a combination of linearly independent solutions that are applicable to any equation. It is comprised of y_n(x), the linearly independent solutions, along with C_n, the arbitrary constants, where n is the order of the differential equation. This equation represents all possible solutions to the homogeneous equation.
Did this research project receive funding support (Spark, SURF, Research Abroad, Student Internal Grants, Collaborative, Climbing, or Ignite Grants) from the Office of Undergraduate Research?
No
Included in
Algebra Commons, Analysis Commons, Ordinary Differential Equations and Applied Dynamics Commons
The General Solution Analysis of Homogeneous Linear Equations
The general solution analysis of homogeneous linear equations are any systems of equations in which all constant terms are equal to zero is classified as a homogeneous linear equation. Some key characteristics of homogeneous linear equations are that there are “zero” solutions, where every system has at least a single solution where all variables are zero, also all solutions to any homogenous linear equation is linearly independent, along with having preserved homogeneity, where if any variable (x) may be added to the system, then any scalar multiple of the variable is also a solution. The General solution of any homogeneous linear differential equation is formed by a combination of linearly independent solutions that are applicable to any equation. It is comprised of y_n(x), the linearly independent solutions, along with C_n, the arbitrary constants, where n is the order of the differential equation. This equation represents all possible solutions to the homogeneous equation.