Home > Calculus > Solving Separable Differential Equations

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

Answer 1

Samantha Adkison

# r = Ae^(0.05s) #

We have:

# (dr)/(ds)=0.05r#

Which is a First Order linear separable DE. We can simply separate the variables to get

# int \ 1/r \ dr = int \ 0.05 \ ds #

Then integrating gives:

# \ \ ln | r | = 0.05s + C # # :. | r | = e^(0.05s + C) # # :. | r | = e^(0.05s) *e^C #

And as #e^x >0 AA x in RR#, and putting #A=e^C# we can write the solution as:

# r = Ae^(0.05s) #

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Aurora Alvarado

To find the general solution of the differential equation (dr)/(ds) = 0.05r, you can separate the variables and integrate both sides. Here's the process:

Separate variables: (dr)/(r) = 0.05ds
Integrate both sides: ∫(1/r) dr = ∫0.05 ds
Solve the integrals: ln|r| = 0.05s + C
Solve for r: r = Ce^(0.05s)

Where C is the constant of integration. This equation represents the general solution to the given differential equation.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.