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    Solutions of differential equations not obtained by giving particular values to the constant of integration in the general solution

    Perry, Thomas Benton
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    [PDF] SolutionsDifferentialEquations.pdf (10.54Mb)
    Date
    1903
    Format
    Thesis
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    Abstract
    In considering the solution of Differential Equations, let the equation be taken in the form f(x,y,p)=c, in which p denotes dy/dx, and f is a rational, integral, and algebraic function of x, y, and p of degree n in p. It has been shown that, in general, this equation must have a solution in the form F(x,y,c)=0. F will always be a function of x, y, and a variable parameter, c. F will also be of degree n in c, but may not be, in all cases, a rational, integral, and algebraic function in x and y. We can assume f an indecomposable function. Then F will also be indecomposable. For if F could be factored, then to each of these factors would correspond a factor of f. There are, in some cases, solutions which can not be obtained by assigning particular values to the constant of integration in the general solution. Such a solution of a Differential Equation is called a Singular Solution.
    URI
    https://hdl.handle.net/10355/15470
    https://doi.org/10.32469/10355/15470
    Degree
    M.A.
    Thesis Department
    Mathematics (MU)
    Rights
    OpenAccess.
    This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
    Collections
    • 1900-1909 Theses (MU)
    • Mathematics electronic theses and dissertations (MU)

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