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FP3 First order differential equations watch

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    (Original post by aymanzayedmannan)
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    (Original post by Zacken)
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    I think that I've got the general formula thing now (after you both said it many times haha) which seems way quicker than having to multiply out! Thanks guys!!!
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    (Original post by kawehi)
    I think that I've got the general formula thing now (after you both said it many times haha) which seems way quicker than having to multiply out! Thanks guys!!!
    Thank Ayman only.
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    (Original post by Zacken)
    Go write some music, enough maths. :rock:
    It's 1 am - I should be heading to sleep I have done 0 maths today though

    what do you plan on doing tomorrow by the way? up for an FP2 mock during the weekend?
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    (Original post by aymanzayedmannan)
    It's 1 am - I should be heading to sleep I have done 0 maths today though

    what do you plan on doing tomorrow by the way? up for an FP2 mock during the weekend?
    ...good idea.

    Yes! Tell me when you do yours so I can as well.
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    (Original post by kawehi)
    I think that I've got the general formula thing now (after you both said it many times haha) which seems way quicker than having to multiply out! Thanks guys!!!
    No worries! Glad we helped

    (Original post by Zacken)
    Thank Ayman only.
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    (Original post by kawehi)
    I'm having some trouble with getting the general solutions of these differential equations! They should be pretty easy, they're at the start of the misc ex

    x \frac{dy}{dx} + (x+1)y = 1

    and for -1<x<1

    (1 + x^2)\frac{dy}{dx} -xy +1 = 0

    If someone could post a method for one of them, it would be super helpful! Thank you!
    IF for the first one will be  e^{\int \frac{x+1}{x} \mathrm{d}x}} .

    Remember that  \frac{x+1}{x} = 1 + \frac{1}{x}
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    (Original post by aymanzayedmannan)
    If this is a 1st ODE,

    \displaystyle \frac{\mathrm{d} y}{\mathrm{d}x} + Py = Q \ \text{(I)}

    Then the general solution can be written as

    \displaystyle \text{General solution:} \ e^{\int P \mathrm{d}x}y = \int e^{\int P\mathrm{d}x}Q \ \mathrm{d}x

    where e^{\int P \mathrm{d}x} is the integrating factor. (Click on the annotated video to see the proof!)

    Once you've got it in the required form as in (I) (which you can do using TeeEm's hint), you should find the integrating factor and then the general solution should be a cinch to find from there!
    You have come up in the world it seems. \mathrm masterrace
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    (Original post by Louisb19)
    IF for the first one will be  e^{\int \frac{x+1}{x} \mathrm{d}x}} .

    Remember that  \frac{x+1}{x} = 1 + \frac{1}{x}
    You snooze, you lose.

    (Original post by Louisb19)
    You have come up in the world it seems. \mathrm masterrace
    :rofl: I'm dying. :rofl:
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    (Original post by Zacken)
    You snooze, you lose.



    :rofl: I'm dying. :rofl:
    Takes about a year to tex dy/dx but it looks so pretty
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    (Original post by Louisb19)
    You have come up in the world it seems. \mathrm masterrace
    :rofl: thank you
 
 
 
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