Kyle Parrott said:Hi there, I know that when I am to guess a solution to to a polynomial for g(t) that I guess Ax^n + Bx^n-1... when the highest power of the polynomial is n but what is my guess supposed to be if the power of n is negative?
ex.
y'' + 4y' + 4y = t^-2*e^(-2t)
so far my guess is,
A*e^(-2t)(B*?...)
Undetermined coefficients refer to the coefficients that are unknown in a polynomial or equation. They are typically represented by letters such as a, b, c, etc. and are used to solve for the unknown values.
In science, undetermined coefficients are commonly used to solve differential equations, which are equations that involve an unknown function and its derivatives. They are also used in regression analysis to find the best fitting line or curve for a set of data.
The process for solving equations using undetermined coefficients involves first identifying the unknown coefficients in the equation. Then, a set of equations is formed by plugging in different values for the unknown coefficients. Finally, the equations are solved simultaneously to find the values of the unknown coefficients.
Determined coefficients are known values that are already specified in an equation, while undetermined coefficients are unknown values that need to be solved for. Determined coefficients are typically represented by numbers, while undetermined coefficients are represented by letters.
While undetermined coefficients can be effective in solving equations and finding unknown values, they may not always provide accurate results. In some cases, the equations may have multiple solutions or no solutions at all, making it difficult to determine the correct values for the unknown coefficients.