# Solving a hard DE: R'(t)=k*4*pi*R(t)^2

• Mathman2013

#### Mathman2013

Homework Statement
solving the following ODE (Hard)
Relevant Equations
R'(t)=k*4*pi*R(t)^2
I have the following DE, R'(t) = k*4*pi*R(t)^2, where R(0) = 5, and R'(0) =-0.001. I have attempted to solve it Maple, and would like to know if I have done it correctly? Last edited by a moderator:
would like to know if I have done it correctly
The way to check that you (Maple?) have done it correctly is to differentiate twice and see if it matches !
You don't need PF to do that for you, do you ?

 and what about entry 1 ?
[edit2] Strike the 'twice'  .

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Last edited:
The way to check that you (Maple?) have done it correctly is to differentiate twice and see if it matches !
You don't need PF to do that for you, do you ?

 and what about entry 1 ?

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I can't find k if I select entry 1.

How wold you go about if you had to solve this DE yourself ?

You mention 'hard' but it really isn't difficult ...

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The way to check that you (Maple?) have done it correctly is to differentiate twice and see if it matches !
The DE is first order, so the OP needs only to differentiate the solution function once.

• BvU
This DE is solvable by hand. Notice that the original equation can be written as
dR/R^2 = Constant*dt

• Oops ! sorry.