Econ6003

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Differential equation

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An equation containing a derivative of a function

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Initial conditions

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Provide the means to determine the value of constants that are contained in the general solutions of differential equations

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General expression for ordinary differential equations

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Number of initial conditions and derivatives for an nth order differential equation

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General form of nth order linear differential equation

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Reduced form of nth order linear differential equation

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Theorem for general solutions to general form of linear differential equation

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What guarantees the existence of y_c and y_p in linear differential equation?

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Initial conditions required for solution for an nth order linear differential equation

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General form of first order linear differential equation

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General solutions for a linear first order differential equation

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Hint 11

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Procedure to solve for y(t)

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General form of linear differential equations with constant coefficients

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A particular solution for linear differential equations with constant coefficients and term

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Hint 14

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Special cases for particular solution. for i=0, i=n

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A particular solution for a second order equation

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Hint 16

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Forming the characteristic equation for linear differential equations with constant coefficients

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Meaning of repeated root

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Complementary function for linear differential equation with constant coefficients

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Derive real root using characteristic equation

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Find roots for this second order equation

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Hint 21

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Procedure for solving linear differential equations with constant coefficients and terms

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Stability of solutions to constant coefficient linear differential equations

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Stability condition on repeated roots for constant coefficient linear differential equations

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Stationary solution

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Linear approximation of autonomous differential equations

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Hint 26

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Linear approximation theorem

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Hint 27

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Difference equation

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General form of a difference equation

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Order of a difference equation

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Difference between differential and difference equations in what n initial conditions specifies

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General form of first order linear difference equations with constant coefficient and term

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General form of linear difference equations with constant coefficient and term

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A particular solution for a linear difference equation with constant coefficient and term

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Hint 34

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Characteristic equation for linear difference equation with constant coefficients

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Complementary function for linear difference equation with constant coefficients

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Complementary function for first order difference equation

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Complementary function for second order difference equation

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Hint 38

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Procedure for solving linear difference equations with constant coefficients

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Stability of solutions to constant coefficient linear difference equations

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Hint 40

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Graphical representation of linear difference equation converging on equilibrium

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Method of undetermined coefficients for finding the particular solution for differential equations with non-constant term of form:

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Method of undetermined coefficients for difference equations with a non-constant term, of form

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