Well, what happened when you tried to work with your guess?kraigandrews said:Homework Statement
I am stuck on this and just need to know the form of the solution for undetermined coeffecients of y''+y'+y=(1-e^-t)
my guess is A-Ae^-t but I am not sure
The undetermined coefficient method is a technique used to solve non-homogeneous linear differential equations. It involves finding a particular solution by assuming the form of the solution and then solving for the coefficients.
The undetermined coefficient method is typically used when the differential equation is non-homogeneous and the non-homogeneous term has a specific form, such as a polynomial or trigonometric function.
The undetermined coefficient method involves assuming a particular solution in the form of the non-homogeneous term and its derivatives, and then solving for the coefficients using substitution and comparison of coefficients with the original equation.
The undetermined coefficient method is limited to solving linear differential equations with non-homogeneous terms that have a specific form. It cannot be used for non-linear differential equations or non-homogeneous terms with more complex forms.
Some tips for using the undetermined coefficient method effectively include: identifying the form of the non-homogeneous term, making sure the particular solution does not overlap with the homogeneous solution, and using a table or chart to organize the coefficients and their corresponding terms.