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## Homework Statement

I was working on an assignment and when I got my draft back, my teacher said I've made some errors working this out, however I'm not sure what I did wrong...

Find the intergral function of:

dy/dt=a(q-y) where t ≥0, y(0)=0 a and q are constants.

## Homework Equations

## The Attempt at a Solution

[itex]\frac{dy}{dt}[/itex]=a(q-y)

[itex]\frac{dy}{}[/itex]=a(q-y)dt

[itex]\frac{dy}{(q-y)}[/itex]=adt

[itex]\int\frac{dy}{(q-y)}[/itex]=[itex]\int adt[/itex]

ln(q-y)=at+c

q-y=e

^{at}+e

^{c}where: e

^{c}is a constant so let it = A

q-y=Ae

^{at}

-y=Ae

^{at}-q

[itex]\frac{-y}{-1}[/itex]= -(Ae

^{at}) [itex]\frac{ (-q)}{-1}[/itex]

y= -Ae

^{at}+ q

∴ y= -Ae

^{at}+ q

Can anyone see any mistakes?