Question

How to you find the general solution of `(dr)/(ds)=0.05s`?

Answer 1

`r=0.025s^2+C`

Explanation:

We should first separate the variables. This means we want to place all terms with `r` on one side of the equation and all terms with `s` on the other.

To do this, we can treat the differential `(dr)/(ds)` like division, meaning we can multiply both sides of the equation by `ds` to "move it" to the right side. That is, we can say that:

`dr=0.05scolor(white).ds`

Now we integrate both sides to undo the differentials:

`intdr=int0.05scolor(white).ds`

`intdr=0.05intscolor(white).ds`

`r=0.05(s^2/2)+C`

`r=0.025s^2+C`