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How does the following differential from the first line become equal to the second line ?

This is confusing me as I do not know where the 3 has come from.

enter image description here

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    $\begingroup$ $1 + 1/2 = 3/2$ $\endgroup$ – eyeballfrog Aug 13 at 23:22
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    $\begingroup$ What worries me is that it looks like the $e^{-x/2}$ became $e^{-x/3}$. $\endgroup$ – Gerry Myerson Aug 13 at 23:46
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    $\begingroup$ Yes that’s true must be a mistake $\endgroup$ – Dan Aug 13 at 23:57
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Isolate $e^{-x/2}$
Then you have $e^{-x/2}(-1 - \frac{1}{2}+\frac x2) = e^{-x/2}(-\frac32+\frac x2) = \frac{1}{2}e^{-x/2}(x-3)$

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  • $\begingroup$ Thank you I understand now $\endgroup$ – Dan Aug 13 at 23:25
  • $\begingroup$ You're welcome! $\endgroup$ – Ak19 Aug 13 at 23:27

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