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

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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