Final answer:
To find a particular solution y using the Method of Undetermined Coefficients, assume the solution has the form y = Aeˣ and equate coefficients to find the value of A.
Step-by-step explanation:
To find a particular solution y of the equation y" + 12y = 3eˣ using the Method of Undetermined Coefficients, we assume that the solution has the form y = Aeˣ, where A is a constant.
Substitute this assumed solution into the differential equation and its derivatives, and equate coefficients. This will give us the value of A and hence the particular solution y.
Once we have found the particular solution, we can combine it with the general solution of the homogeneous equation (y" + 12y = 0) to obtain the complete solution of the given equation.