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Numerade Educator

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Problem 6 Medium Difficulty

Solve the differential equation.
$ y' - y = e^x $

Answer

$$
y=(x+C) \cdot e^{x}
$$

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Video Transcript

The first step to solving the differential equation is to multiply both sides by the integrating factor. So in this context, the integrating factor eed to the integral of negative one detox integrate negative one. We get e to the negative one X Now we know we're gonna multiply. We're gonna be multiplying this throughout the equation, Which means we have now each the negative acts. Do you? Why over jacks? Plus why times d of e to the negative axe divided by D backs is eat the X minus acts which is eating zero. Now we actually know anything to the earth. Power is one, regardless of what we have on the bottom sign, which means we now hop this and then remember, we could enter it with both sides with respect, tow X. So we simply have why I eat the night of maximal left inside is now the integral of one is X and I remember when we integrate, we always have the constant integration would just see. So this could be written simply in terms of why, as y equals acts plus c times E to the X