perplexus.info :: Calculus : Given the Expression, Find the Function

Given the Expression, Find the Function (Posted on 2024-05-24)

Determine f(x), given that:

f'(x) = 2 - f(x)/x

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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another substitution

| Comment 2 of 3 |

We have: f'(x) = 2 - f(x)/x

A different substitution also works:

Let h(x) = x*f(x)

h'(x) = f(x) + x*f'(x)

= f(x) + 2x - f(x)

= 2x

h(x) = x^2 + C

f(x) = h(x)/x = x + C/x

Posted by Larry on 2024-05-24 14:40:36

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