Question

Find the solution of the differential equation, and then solve for the initial condition

mathImg.php?%5Cdisplaystyle%7Bx%7D%7B%5CmathImg.php?%5Cdisplaystyle%7By%7D%7B%5C

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Answer #1

Hi..

The way we solve this is by separating the variables and the dy from the dx and integrate both sides. Once we have done that we will plug in our initial condition and solve for c.

mathImg.php?%5Cdisplaystyle%7Bx%7D%7B%5C

The left side turns into mathImg.php?%5Cdisplaystyle%7B%7Bx%7D%7D

The right side turns into mathImg.php?%5Cdisplaystyle%7B%5Cleft(%5

And then we plug 1 in for x and y and solve for c

We get mathImg.php?%5Cdisplaystyle%5Cfrac%7B%7B

We get c = -19/12

Our answer is

mathImg.php?%5Cdisplaystyle%7B%7Bx%7D%7D

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