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

1 Answer
Dec 3, 2016

#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#