QQuestionMathematics
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
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Answer
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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 $(D - 1)(D - 3)$.
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