What functions $f$ satisfy the equation $$f'(x)=\frac{f(\sqrt{1-x^2}) - f(x)}x$$
Could you kindly show how you arrived at the function?
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Bumblebee
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David Okogbenin
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Thanks for editing it. I didn’t really know how – David Okogbenin Mar 21 '20 at 19:05
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1This might be help you in future. – Bumblebee Mar 21 '20 at 19:11
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1Hint: Note that $$f'(\sqrt{1-x^2})=-\dfrac{x}{\sqrt{1-x^2}}f'(x).$$ Use this to find $f'$ and then integrate. – Bumblebee Mar 21 '20 at 19:15
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Thanks again – David Okogbenin Mar 21 '20 at 19:17
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When u say f’((1-x^2)^1/2) are u referring to the derivative with respect to x or to (1-x^2)^1/2 – David Okogbenin Mar 21 '20 at 21:20
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@Bumblebee Can you add more detail? I don't see how this helps. – Aligator Mar 21 '20 at 21:39
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@DavidOkogbenin with respect to $x$ – Aligator Mar 21 '20 at 21:45
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@Soheil but shouldn’t the left hand side be with respect to (1-x^2)^1/2. – David Okogbenin Mar 21 '20 at 22:12
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And how does it even help either way – David Okogbenin Mar 21 '20 at 22:13
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@DavidOkogbenin I dont know I am confused – Aligator Mar 21 '20 at 22:26
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@Bumblebee Can you show the steps to get that? I don't think it's true. – empCarnivore Mar 21 '20 at 23:51