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Help: Functional Equation 2

Moderator's edit:

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

Note by Akhilesh Prasad
10 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... Rishabh Cool · 10 months ago

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@Rishabh Cool Thanks a lot for clarifying that out had been banging my head like crazy. Akhilesh Prasad · 10 months ago

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@Rishabh Cool So it was \(f^{ 2 }\left( x \right) ={ (f\left( x \right) ) }^{ 2 }\) not \(f^{ 2 }\left( x \right) ={ f^{ '' }\left( x \right) }\) Akhilesh Prasad · 10 months ago

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@Akhilesh Prasad Yeah.... Thanks to moderator's edit.... :-} Rishabh Cool · 10 months ago

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@Aareyan Manzoor Akhilesh Prasad · 10 months ago

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@parv mor Akhilesh Prasad · 10 months ago

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