Question

Find a particular solution to the ODE 4y′′ − 8y′ + 40y =
36(x²)(eˣ). Show all work.

Answer 1

To find a particular solution to the given ODE, we can use the method of undetermined coefficients.

Step-by-step explanation:

To find a particular solution to the given ODE, we can use the method of undetermined coefficients. Assuming that the particular solution is of the form y = Ax²eˣ, we can substitute this solution into the ODE to find the value of A.

First, differentiate y twice with respect to x to find y′′ and y′. Substitute these expressions along with y into the ODE and equate it to the given function 36x²eˣ. Solving the resulting equation, you will find the value of A.

Finally, substitute the value of A into the particular solution y = Ax²eˣ to obtain the particular solution to the ODE.