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Cross multiplying our equation, we have that

Now we integrate. The right hand side integrates to

As for the left hand side, we integrate by partial fractions.

Now we can either compare coefficients or plug in values for x. I will choose to plug in values for x. The above tells us that

when , we have that

and so . When , we have

and so . Hence, we have

(technically the above should add a constant but we can include this in a minute.) Hence

becomes

Using the initial condition of , we see that our constant is

and simplifying, this becomes

Our equation simplifies to

Exponentiating the far left and the far right hand sides of the above gives

Taking the tenth root of both sides yields

Removing the absolute values, we have

Plugging in the initial condition of , we see that only the positive value above works. Hence

Now, we cross multiply to see that

Bringing the values to one side gives

Lastly, isolating for gives

completing the question.
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