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# Differential Equation watch

1. So I had this question which I got from the new spec sample paper. There is this differential equation which you have to solve.

It says show that he solution general solution to the differential equation can be written in the form where A is an arbitrary positive constant.

You have to find the general solution to it. I have tried multiple ways and tried to see if any work but with no luck. Need someone to help me out here

Also note:
If is a constant then is also a constant.
3. You can seperate it into:

then integrate after using partial fractions on the LHS.
4. (Original post by Edgemaster)
You can seperate it into:

then integrate after using partial fractions on the LHS.
That is exactly what I was thinking. Anyway, I did the following and still can't seem to get the answer. Here is what I did

Somehow can't get the answer because either I have done it wrong or I can't evaluate and simplify.
That is exactly what I was thinking. Anyway, I did the following and still can't seem to get the answer. Here is what I did

Somehow can't get the answer because either I have done it wrong or I can't evaluate and simplify.
It appears you either did the partial fractions incorrectly or the integrating incorrectly.
That is exactly what I was thinking. Anyway, I did the following and still can't seem to get the answer. Here is what I did

Somehow can't get the answer because either I have done it wrong or I can't evaluate and simplify.
Can you show us the complete working for partial fractions?
7. (Original post by Edgemaster)
Can you show us the complete working for partial fractions?

Remember that you have 500 outside of the integral. Multiplying this through gives:

9. (Original post by IWantIPods)
Remember that you have 500 outside of the integral. Multiplying this through gives:

I did that if you look at my first working out I posted. I just don't know what I've done wrong here or whats wrong in the integration.
I did that if you look at my first working out I posted. I just don't know what I've done wrong here or whats wrong in the integration.

Integrating this gives:

11. (Original post by IWantIPods)

Integrating this gives:

Ah, I see what I did wrong there. Let me redo and see what I get.
12. nvm. Still not there. I get somewhere like

I still cant get the answer -_-' Something else I am missing?
nvm. Still not there. I get somewhere like

I still cant get the answer -_-' Something else I am missing?
Your transition from line 1 to line 2 is incorrect.

then using the fact that:

then anti-log both sides of the equation.
14. (Original post by IWantIPods)
Your transition from line 1 to line 2 is incorrect.

then using the fact that:

then anti-log both sides of the equation.
I did do that the first time around but didn't get the answer so I used the other one which was again wrong.

but I can't seem to simplify this to the required answer.
I did do that the first time around but didn't get the answer so I used the other one which was again wrong.

but I can't seem to simplify this to the required answer.
Let
16. (Original post by IWantIPods)
Let
I did this but I don't think it makes a big difference.

Therefore,
I did this but I don't think it makes a big difference.

Therefore,
Look at what the question is asking you to prove. The numerator is 50A where A is a constant. Just divide the numerator and the denominator by .

Also, in the denominator, you should have not .
18. (Original post by IWantIPods)
Look at what the question is asking you to prove. The numerator is 50A where A is a constant. Just divide the numerator and the denominator by .

Also, in the denominator, you should have not .
My bad. I mistyped that but I see what you mean. Didn't read the question properly.

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