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Numerade Educator

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Problem 10 Medium Difficulty

Solve the differential equation.
$ \frac {dz}{dt} + e^{t+z} = 0 $

Answer

$z=-\ln \left(e^{t}+C\right)$

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Video Transcript

this question asked us to solve the differential equation. Deasy over DT is added to eat the cheap list Z equivalent to zero. No, first things first is we want to get all Izzy's on the left hand side and all the teasing, the right hand side or vice versa. But the point being you two have the same variable on the same side, and that had the other variable on the other side. Now we know we can try to get rid of the fraction over here by writing this in terms of negative exponents because it makes it easier because we're gonna integrate. Okay, No, When we integrate, we know that on the left hand side, we simply add a negative sign is kind of a special case on the right hand side, it literally just stays the same. And then we can add or unknown constant Now, multiply the equation by negative one, multiply by natural law because remember, natural log times e gives us one. Then lastly, we wanted in terms of positive seed, not negative c So you see, our negative Z becomes positive, See, because we're multiplying by negative one on each side, we end up with their final suit