# Initial value problem

## Homework Statement

Solve each of the following initial value problems: a) f'(x)=(x2-1)/x5 f(1/2)=3

## The Attempt at a Solution

I guess my problem with this is I'm not 100% sure what I'm being asked to do. I know I need to use integration to find the original function. Ok no prob I got -1/2x-2+1/4-4. So after that am I just supposed to plug in 3=the original function, substituting 1/2 for x? That doesn't seem right since I'm not getting 3... Am I doing the question incorrectly or have I done my integration wrong?

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You're leaving out the whole problem. Did the question say f(1/2) = 3? Or f(3) = 1/2? As far as your integral goes, it looks fine to me if you mean $$\frac{-1}{2x^2}+\frac{1}{4x^4}$$. However, don't forget to add a constant everytime you take an integral, so just put a +C at the end. After that, just plug in the x and f(x) values to solve for C.