Question

For the differential equation "y double prime minus 4y prime plus 4y equals e raised to the power of 2x," use the method of undetermined coefficients to find the particular solution.

a) y sub p of x equals x squared e raised to the power of 2x
b) y sub p of x equals x e raised to the power of 2x
c) y sub p of x equals e raised to the power of 2x
d) y sub p of x equals x squared e raised to the power of x

Answer 1

The particular solution to the given differential equation using the method of undetermined coefficients is yp(x) = (1/4)e2x.

Step-by-step explanation:

To find the particular solution to the given differential equation, we can use the method of undetermined coefficients. The particular solution can be written as a linear combination of exponential functions, polynomials, and trigonometric functions.

In this case, the particular solution is of the form yp(x) = Ae2x, where A is a constant to be determined.

To find the value of A, we substitute the particular solution into the given differential equation and solve for A. Substituting the particular solution into the differential equation yields 4Ae2x - 8Ae2x + 4Ae2x = e2x. By simplifying the equation, we find that A = 1/4. Therefore, the particular solution to the given differential equation is yp(x) = (1/4)e2x.