Determine f(x), given that:
f'(x) = 2 - f(x)/x
Another way: assume a polynomial
f(x) = ax^2 + bx + c + d/x + e/x^2
f'(x) = 2ax + b - d/x^2 - 2e/x^3
f'(x) = 2 - f(x)/x = 2 - ( ax + b + c/x + d/x^2 + e/x^3 )
2ax + b - d/x^2 - 2e/x^3 = -ax + (2-b) - c/x - d/x^2 - e/x^3
2a = -a --> a=0
b = 2-b --> b=1
c not on LHS--> c=0
-d/2 = -d --> d can be anything
-2e = -e --> e=0
Conclusion: f(x) = x + anything/x = x + k/x
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Posted by Larry
on 2024-05-24 15:01:14 |
other method
