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Solve the differential equation.

$ y' = x - y $

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

Differential Equations

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in order to solve this equation. The first step is to check out the integrating factor in this case, we have eat the integral off one deep acts which we know gives us integrating factor of simply eat the axe Pretty straightforward, Which means now multiplying this by every term in the original equation. We end up with this equation right over here. Now, given this, we know we can take the integral off the right hand side to have why eat the axe is the integral of acts e to the axe de ax that you may have learned integration by parts, which is a method you could use here. There's also U substitution interaction by parts makes more sense in this context. So integrating buy parts Well, we still have the same thing on the left hand side. That doesn't change. So integrating this buy parts, breaking it apart. We have X each the axe minus e to the ax, plus c now final step. When we solve we wanted just in terms of a singular why we don't want anything untouched. The why, which means divided to turn by either the X, we have wise X minus one pussy over E to the X Now I'm gonna also right. This is why is X minus one Cost C e to the negative X. These are equivalent.