A function minus its derivative

A function $f$ satisfies $f(x) - f'(x) = (x+1)^3$ with $f(0) = 16$ . Find $f(9)$ .

Show hints (2)+

Try a polynomial particular solution - a cubic in $(x+1)$ - and match coefficients against $(x+1)^3$ .
Add $Ke^x$ and use $f(0)=16$ ; it forces $K=0$ . Then evaluate at $x=9$ .

Answer

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1366

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