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Numerade Educator

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Problem 5 Medium Difficulty

Solve the differential equation.
$ y' + y = 1 $

Answer

$$y=1+C e^{-x}$$

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Video Transcript

the first step to solving a differential equation is to find the integrating factor. So we have aged the integral of p of X dx, which in this case is just one D axe which gives us e to the X When we integrate, the integral of one would be, in this context the variable which is acts. Therefore, we're now multiplying this it back into the original equation. So we end up with each the axe. Do you Why over D backs, Plus why times eat the acts. Like I said, we're multiplying all the factors by this we're sending this equal to eat of the axe. Now we need to solve for y right, cause the question said to solve the equations or our end solution is gonna be why equals something. So in this context, we end up with y equals one because we're dividing each of these terms by eating the X. So we end up with one over here because of the extra. I bet you next is just one plus c and then divided by E to the X, which could also be written a c e to the negative x, the negative power when we're writing it on one line