# Help: Functional Equation 2

Moderator's edit:

Find a continuous function $$f(x)$$ not everywhere zero such that $$\displaystyle (f(x))^2 = \int_0^x \dfrac{f(t) \cdot \sin t}{2 + \cos t} \, dt$$.

2 years, 5 months ago

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What's the problem?? Just differentiate it to get: $2 f(x) f'(x)=\dfrac{f(x) \sin x}{2+\cos x}$ Now for f(x)$$\neq$$0, we can write : $2f'(x)=\dfrac{\sin x}{2+\cos x}$ Now integrate both sides to get f(x) which is very easy...

- 2 years, 5 months ago

Thanks a lot for clarifying that out had been banging my head like crazy.

- 2 years, 5 months ago

So it was $$f^{ 2 }\left( x \right) ={ (f\left( x \right) ) }^{ 2 }$$ not $$f^{ 2 }\left( x \right) ={ f^{ '' }\left( x \right) }$$

- 2 years, 5 months ago

Yeah.... Thanks to moderator's edit.... :-}

- 2 years, 5 months ago

- 2 years, 5 months ago