Algebra
# Functional Equations

The function \(f \) satisfies \[(x-y)f(x+y)-(x+y)f(x-y)+4xy(x^2-y^2)=0,\]

whenever \( |x| \neq |y | \).

Given that \(f(1)=2,\) what is \(f(x)\)?

A function \(f\) from the positive integers to the positive integers satisfies the conditions

1) \(f(n) = 2 f(n-1) + 3 \),

2) \( f(1) = 9 .\)

What is the value of \( f(9) \)?

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