Question

(1/(D-m))f(x), where D=d/dx and m is constant, is equal to​

Answer 1

SOLUTION

TO DETERMINE

$\displaystyle\sf{ \frac{1}{D - m} f(x) \: \: \: where \: \: \:D \equiv \frac{d}{dx} }$

Where m is constant

EVALUATION

We know that D is a differential operator

$\displaystyle\sf{ \:D \equiv \frac{d}{dx} }$

Now we have to simplify the expression

$\displaystyle\sf{ \frac{1}{D - m} f(x) \: \: \: where \: \: \:D \equiv \frac{d}{dx} }$

We have

$\displaystyle\sf{ \frac{1}{D - m} f(x) \: \: }$

$\displaystyle\sf{ = {e}^{mx} \int \: f(x) {e}^{ - mx} \: dx}$

The above concept is used in finding particular integral of a differential equation

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