When can undetermined coefficients be used?
Undetermined Coefficients (that we learn here) which only works when f(x) is a polynomial, exponential, sine, cosine or a linear combination of those. Variation of Parameters which is a little messier but works on a wider range of functions.
When can undetermined coefficients not be used?
The method of undetermined coefficients could not be applied if the nonhomogeneous term in (*) were d = tan x. So just what are the functions d( x) whose derivative families are finite? See Table 1. Example 1: If d( x) = 5 x 2, then its family is { x 2, x, 1}.
When can I not use method of undetermined coefficients?
What is undetermined coefficient?
The Method of Undetermined Coefficients In order to give the complete solution of a nonhomogeneous linear differential equation, Theorem B says that a particular solution must be added to the general solution of the corresponding homogeneous equation.
When to use undetermined coefficients in second order nonhomogeneous differential equations?
If the nonhomogeneous term d ( x) in the general second‐order nonhomogeneous differential equation is of a certain special type, then the method of undetermined coefficients can be used to obtain a particular solution.
How do you modify a family with undetermined coefficients?
The “offending” family is modified as follows: Multiply each member of the family by x and try again. Since the modified family no longer contains a solution of the corresponding homogeneous equation, the method of undetermined coefficients can now proceed.
How do you find the coefficient of a differential equation?
The method is quite simple. All that we need to do is look at g(t) g ( t) and make a guess as to the form of Y P (t) Y P ( t) leaving the coefficient (s) undetermined (and hence the name of the method). Plug the guess into the differential equation and see if we can determine values of the coefficients.