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.
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...
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...
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...
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...
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)...