Working Rules For Finding Particular Integral For Differential Equations (MM-10.2-20)

Solve the differential equation
y''' + 3y'' +7y' +5y = 16e^(-x)cos 2x y(0) = 2, y'(0) = - 4, y''(0) = - 2

[nikko]

I still don’t understand how this happens, but it’s very interesting. This method is similar to the Laplace transform, but without solving the Cauchy problem