Another Functional Equation #2

Algebra Level 4

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

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

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

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

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