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# MEI C4 Differential Equations

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1. Obtain a particular solution to (1-e^2y)dy/dx = e^y

Given that y=1 when x=2.
There is no need to express y in terms of x.

Any ideas?

2. (Original post by Pheylan)

carry on..
3. (Original post by ziedj)
carry on..

4. (Original post by Pheylan)

You have passed the test. One internet will be sent your way.
5. Solved the solution up to substituting the x and y values and was about to post when i scrolled down and saw Pheylan's answer
6. (Original post by Pheylan)

so is x + e^-y + e^y = 4 the particular solution?
7. (Original post by Hippysnake)
so is x + e^-y + e^y = 4 the particular solution?
this is:
(Original post by Pheylan)

8. (Original post by Hippysnake)
so is x + e^-y + e^y = 4 the particular solution?
where did 4 come from?
9. (Original post by time.to.dance)
Solved the solution up to substituting the x and y values and was about to post when i scrolled down and saw Pheylan's answer
sorry

x^2 dy/dx - y^2 =0?

I end up with y = x + c but that seems a bit too easy...

11. (Original post by Pheylan)

I got x/1+cx?

Ah well, I have one more question?

At time t seconds the rate of increase in the concentration of flesh eating bugs in a controlled environment is proportional to the concentration C of bugs present. Initially C= 100 bugs and after 2 seconds there are five times as many.

Write down a differential equation connection dC/dt, C and t and hence find an expression for C in terms of t.

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