How do I integrate dy/dt=ay-b in differential equations?

[agent_509]

I am just getting started on learning differential equations, and I'm stuck on this one:

dy/dt=ay-b​

the book tells me to factor out the a, and then divide

dy/dt=a(y-b/a)

(dy/dt)/(y-b/a)=a​

This is where I get stuck, it completely skips over what to do next and just says to integrate both sides, and you come up with this

ln | y – (b/a) | = at + c
​

I multiplied both sides by dt to get

[1/(y-b/a)]dy=a dt​

but I don't see how integrating both sides gets the above equation, I instead get

ln(ay-b)=at+c​

what am I doing wrong?

 

[agent_509]

never mind, I'm an idiot, thanks