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The particular integral of $\left(D^4 - D^3 - 9D^2 - 11D - 4\right)y = e^{-x}$, where $D = \frac{d}{dx}$, is:}

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Whenever $f(a)=0$, instead of factoring the entire polynomial, keep multiplying the expression by $x$ and differentiating the denominator with respect to $D$ until a non-zero denominator value is encountered upon substitution of $D=a$.

Updated On: Jun 25, 2026

$-\frac{x^2 e^{-x}}{20}$
$-\frac{x e^{-x}}{15}$
$-\frac{x^3 e^{-x}}{30}$
$-\frac{e^{-x}}{10}$

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The Correct Option is C

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The particular integral of $\left(D^4 - D^3 - 9D^2 - 11D - 4\right)y = e^{-x}$, where $D = \frac{d}{dx}$, is:}

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The Correct Option is C

Solution and Explanation

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