Find the particular solution that satisfies the given initial condition.

This differential equation can be solved by separating the variables.

Dividing by e^r and multiplying by ds results in the variables r and s on the different sides of the equation:

This is equivalent to

Now we can take the integral of the both sides of the equation:

 , where C is an arbitrary constant.

From here, 

This differential equation can be solved by separating the variables.

Dividing by e^r and multiplying by ds results in the variables r and s on the different sides of the equation:

This is equivalent to

Now we can take the integral of the both sides of the equation:

 , where C is an arbitrary constant.

From here, 

and 

or 

Since the initial condition is r(0) = 0, we can find the constant C:

This means 

and 

Plugging C in in the equation for r(s) above, we can get the particular solution:

 . This is algebraically equivalent to

 . This is the answer.