Is this project an undergraduate, graduate, or faculty project?

Undergraduate

individual

Authors' Class Standing

Jose Rolando Gonzalez, Sophomore

Lead Presenter's Name

Jose Rolando Gonzalez

Faculty Mentor Name

Acharya, Keshav R.

Abstract

The main focus of this paper is that in which the nonlinearity does not occur in the highest differentiated term.This paper will further discuss one observed method. The method to be presented has the particular advantage that its wide scope and application, yet it is constrained to differential equations that are associated with nonconservative systems.We wish to extend the results of [2] to all real numbers in the domain of x. The Ermakov-Pinney method of lineraization was employed to obtain solvable form of the equation. An implicit solution of the nonlinear differential equation y00 + P(x)y = qm(x)=ym is found to be y = jw[(C1 R dx w2 + C2)2 + C3]j 1 1􀀀mjj + C4 if qm(x) = w(x)m􀀀3. Where w is the combination of two linearly independent solutions u and v, such the w(x) = au(x) + bv(x), as well as ' = R w(x)􀀀2dx. Where C1,C2,C3, and C4 are arbitrary constants.

Did this research project receive funding support (Spark or Ignite Grants) from the Office of Undergraduate Research?

Yes, Spark Grant

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INVESTIGATING THE SOLUTIONS TO NON-LINEAR SECOND ORDER DIFFERENTIAL EQUATIONS

The main focus of this paper is that in which the nonlinearity does not occur in the highest differentiated term.This paper will further discuss one observed method. The method to be presented has the particular advantage that its wide scope and application, yet it is constrained to differential equations that are associated with nonconservative systems.We wish to extend the results of [2] to all real numbers in the domain of x. The Ermakov-Pinney method of lineraization was employed to obtain solvable form of the equation. An implicit solution of the nonlinear differential equation y00 + P(x)y = qm(x)=ym is found to be y = jw[(C1 R dx w2 + C2)2 + C3]j 1 1􀀀mjj + C4 if qm(x) = w(x)m􀀀3. Where w is the combination of two linearly independent solutions u and v, such the w(x) = au(x) + bv(x), as well as ' = R w(x)􀀀2dx. Where C1,C2,C3, and C4 are arbitrary constants.