Undetermined coefficients Definition and 5 Discussions

In mathematics, the method of undetermined coefficients is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and recurrence relations. It is closely related to the annihilator method, but instead of using a particular kind of differential operator (the annihilator) in order to find the best possible form of the particular solution, a "guess" is made as to the appropriate form, which is then tested by differentiating the resulting equation. For complex equations, the annihilator method or variation of parameters is less time-consuming to perform.
Undetermined coefficients is not as general a method as variation of parameters, since it only works for differential equations that follow certain forms.

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  1. phantom lancer

    Method of undetermined coefficients -- Help please

    Homework Statement Using the method of undetermined coefficients, determine the general solution of the following second-order, linear, non-homogenous equations. y'' - 4y' + 4y = 2e^(2x+3) Homework Equations I'm not sure what to do from here... Also, I'm new here. How do I use the superscript...
  2. kostoglotov

    Need help understanding an aspect of undetermined coeff's

    imgur link: http://i.imgur.com/8TOXi9t.png I am comfortable with the need to multiply the polynomial in front of e^{2x} by x^3, that makes perfect sense in terms of what the text has already said about how no term in the particular solution should duplicate a term in the complementary solution...
  3. kostoglotov

    Trial solution, undetermined coefficients, 2nd order non-homogeneous equation

    Homework Statement Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients. For: y'' + 2y' + 10y = x^2e^{-x}\cos{3x} There's a modification performed and I'm not 100% confident as to why. Homework Equations The Attempt at a Solution The...
  4. D

    High order differential equations: undetermined coefficients

    Homework Statement If the method of undetermined coefficients is used to find a particular solution yp (t) to the differential equation y'''-y'=te^(-t)+2cos(t) should have the form: ? Homework Equations The Attempt at a Solution LHS r^3-r=0 roots= 0, 1 y_c(t)=c_1e^t RHS...
  5. D

    2nd order differential equation: undetermined coefficients

    Homework Statement y''-y=t-4e^(-t) Homework Equations method of undetermined coefficients The Attempt at a Solution solving for characteristic equation first y''-y=0 r^2-1=0 c_1e^(-t)+c_2e^(t) RHS particular solution t-4e^(-t) y_p(t)= At+B+Ce^(-t) y_pt'(t)=A-Ce^(-t)...