Question

How do I solve the equation `dy/dt = 2y - 10`?

Answer 1

You can use a technique known as Separation of Variables.
Take all the `y` to one side and the `t` on the other...
You get:

`dy/(2y-10)=dt`

Now you can integrate both sides with respect to the correspondent variables:

`int1/(2y-10)dy=intdt`
`int1/(2(y-5))dy=intdt`

And finally
`1/2ln(y-5)=t+c`

Now you can express `y` as:
`ln(y-5)=2t+c`
`y-5=c_1e^(2t)` where `c_1=e^c`
`y=c_1e^(2t)+5`

You can substitute back to check your result (calculating `dy/dt`) remembering that now it is: `y=c_1e^(2t)+5`