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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
1 year, 9 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 - 1 year, 9 months ago

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

Akhilesh Prasad - 1 year, 9 months ago

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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 - 1 year, 9 months ago

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

Rishabh Cool - 1 year, 9 months ago

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@Aareyan Manzoor

Akhilesh Prasad - 1 year, 9 months ago

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@parv mor

Akhilesh Prasad - 1 year, 9 months ago

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