How to start Differential equation

[delsoo]

Mod note: Thread moved from technical math section. The OP has already been notified that this is not a suitable start to a request for homework help.[/color]
can anyone teach me how to start it? i really have no idea.. PART A

 

[HomogenousCow]

You don't need to solve that equation for the two problems
The first problem amounts to finding a stationary point while the second requires you to implicitly differentiate that expression with respect to time.

Just a hint for i), the staionary point may only exist in a certain limit.

 

[delsoo]

can you show the full working for part i please? i'd been thinking of this question for the whole day yet still can't get the ans

 

[HomogenousCow]

Here

Edit: In the last step I just plugged the value of x (which had to be done via a limit since it was positive infinty) back into the original expression for the answer

 

[HomogenousCow]

Note to self: I should really learn LaTeX

 

[delsoo]

if i do this way then how should i proceed ? note: i want to find x first , then sub the value of x which i get into the eqaution 1... after arranging the terms, i would get ln 0 ... then i can't find the value of x ...

 

[HomogenousCow]

At the last step, you need to realize that the only way for the left hand side to equal zero is when x tends to positive infinity.

 

[delsoo]

can anyone help me with this question? i got stucked here.. can you figure out which part contains mistake or post the full solution here? thanks in advance!
http://i.imgur.com/RZpquyd.jpg?1

http://imgur.com/RZpquyd&Eoaa0mm#0