Another Functional Equation #2

Algebra Level 5

$\large{f(x+y) = 3^yf(x) + 2^xf(y)}$

Let $$f(x)$$ be a function where $$f: \mathbb R \to \mathbb R$$ for which $$f(1) = 1$$ such that for all real $$x,y$$, the functional equation above satisfies.

Then find the value of $$f(20) - f(15)$$.

Note: To avoid tediousness, first generalize $$f(x)$$, then use a calculator to find the value asked.

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