Q
QuestionMathematics

Find a linear differential operator that annihilates the given function (use D for the differential operator) e^-x + 7xe^x - x^2 e^x
6 months agoReport content

Answer

Full Solution Locked

Sign in to view the complete step-by-step solution and unlock all study resources.

Step 1
: Identify the given function

The given function is $f(x) = e^{-x} + 7xe^{x} - x^2 e^{x}$.

Step 2
: Find the derivative of the function

\frac{df(x)}{dx} = -e^{-x} + 7e^{x} + 7xe^{x} - 2x e^{x}
In order to find a linear differential operator that annihilates the given function, we first need to find the derivative of the function.

Final Answer

The annihilator for the given function $f(2$) = e^{-x} + 7xe^{x} - x^2 e^{x}$ is $(D - 1)(D - 3)$.