Question

Use undetermined coefficients to find the particular solution to y′′+7y′+12y=3e−2tY(t)=e−3t+2e−4t+23​e−2t​

Answer 1

To find the particular solution to y'' + 7y' + 12y = 3e^(-2t), use undetermined coefficients. The particular solution can be found by substituting Y(t) into the differential equation and solving for the coefficients.

Step-by-step explanation:

To find the particular solution to y'' + 7y' + 12y = 3e^(-2t), we can use undetermined coefficients. The particular solution can be written as Y(t) = Ae^(-3t) + Be^(-4t) + Ce^(-2t). We can determine the values of A, B, and C by substituting Y(t) into the differential equation and solving for the coefficients. By comparing the coefficients of each exponential term on both sides of the equation, we can set up a system of equations and solve for A, B, and C.