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Question

Prove the following identity:
f(x)2xf(x)+13f(0)f(0)=1, if f(x)=3ex3.

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Solution

f(x)=3ex2f(0)=3
f(x)=6xex2f(0)=0
So =f(x)2xf(x)+13f(0)f(0)
=6xex22x(3ex2)+13(3)0
6xex26xex2+1
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