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FP3 First order differential equations

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Reply 20
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!!!
Reply 21
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. :biggrin:
Reply 22
Original post by Zacken
Go write some music, enough maths. :rock:


It's 1 am - I should be heading to sleep :tongue: I have done 0 maths today though :colondollar:

what do you plan on doing tomorrow by the way? up for an FP2 mock during the weekend? :tongue:
Reply 23
Original post by aymanzayedmannan
It's 1 am - I should be heading to sleep :tongue: I have done 0 maths today though :colondollar:

what do you plan on doing tomorrow by the way? up for an FP2 mock during the weekend? :tongue:


...good idea. :redface:

Yes! Tell me when you do yours so I can as well. :biggrin:
Reply 24
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. :biggrin:
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 :smile:

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

and for -1<x<1

(1+x2)dydxxy+1=0(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
Unparseable latex formula:

e^{\int \frac{x+1}{x} \mathrm{d}x}}

.

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

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

Then the general solution can be written as

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

where ePdxe^{\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 :wink:
Reply 27
Original post by Louisb19
IF for the first one will be
Unparseable latex formula:

e^{\int \frac{x+1}{x} \mathrm{d}x}}

.

Remember that x+1x=1+1x \frac{x+1}{x} = 1 + \frac{1}{x}


You snooze, you lose. :wink:

Original post by Louisb19
You have come up in the world it seems. \mathrm masterrace :wink:


:rofl: I'm dying. :rofl:
Original post by Zacken
You snooze, you lose. :wink:



:rofl: I'm dying. :rofl:


Takes about a year to tex dy/dx but it looks so pretty :smile:
Reply 29
Original post by Louisb19
You have come up in the world it seems. \mathrm masterrace :wink:


:rofl: thank you

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