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Math geniuses... help with a simple equation
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| DJ Cinos |
y' + 2y = 6x + 5
If anybody could help me with this I'd be quite happy... I've always had a hard time with this kind of equations. :) |
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| Belgian Bonzai |
y=3x+1
On sight :D |
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| DJ Cinos |
| quote: | Originally posted by Belgian Bonzai
y=3x+1
On sight :D |
That easy? Too bad I lack such eye for maths... how do you solve one of these? :conf:
We had such a rushed maths class I don't think I ever learned it. |
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| Belgian Bonzai |
| quote: | Originally posted by DJ Cinos
how do you solve one of these? :conf: |
Well, since the right-hand-side is a polynom, you can expect y to be polynomial (that derivative changes that part into a polynom [of lower order], added to 2 times a polynom; it just might work). If it were something like Ax²+something (or higher exponent) then y' would be 2Ax+something and you'd never be able to lose the x². So it has the form Ax+B.
Substituting y for Ax+B yields:
A+2(Ax+B)=6x+5
so you get
2Ax=6x which gives you A=3
and
A+2B=5, which (with A=3) gives B=1
So 3x+1 |
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| DJ Cinos |
| quote: | Originally posted by Belgian Bonzai
Well, since the right-hand-side is a polynom, you can expect y to be polynomial (that derivative changes that part into a polynom [of lower order], added to 2 times a polynom; it just might work). If it were something like Ax²+something (or higher exponent) then y' would be 2Ax+something and you'd never be able to lose the x². So it has the form Ax+B.
Substituting y for Ax+B yields:
A+2(Ax+B)=6x+5
so you get
2Ax=6x which gives you A=3
and
A+2B=5, which (with A=3) gives B=1
So 3x+1 |
Thank you! :) Thumbs up! |
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| Sunsnail |
I've had crappy math teachers over the years, also not paying attention the the teachers I had........ how do you do something like
5 = 3
___ ____
4+x 2 |
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| Orbital32 |
i had really crappy teachers. i never got past:
1+1=X |
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| Aquarian |
dy/dx + 2y = 6x + 5
dy = (6x + 5 - 2y)dx
y = 3x^2 + 5x - 2yx
y + 2yx = 3x^2 + 5x
y(1+2x) = 3x^2 + 5x
y = ( 3x^2+5x ) / ( 1 + 2x) |
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| DJ Cinos |
| quote: | Originally posted by Aquarian
dy/dx + 2y = 6x + 5
dy = (6x + 5 - 2y)dx
y = 3x^2 + 5x - 2yx
y + 2yx = 3x^2 + 5x
y(1+2x) = 3x^2 + 5x
y = ( 3x^2+5x ) / ( 1 + 2x) |
The previous poster wasn't correct? :conf:
The answer in this one seems rather complicated. |
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| starglider |
| quote: | Originally posted by DJ Cinos
The previous poster wasn't correct? :conf:
The answer in this one seems rather complicated. |
Plug it back in and you'll see...
y' + 2y = 6x + 5 where y = 3x + 1
(3x + 1)' + 2(3x + 1) = 6x + 5
3 + 6x + 2 = 6x + 5
6x + 5 = 6x + 5 |
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| DJ Cinos |
| quote: | Originally posted by starglider
Plug it back in and you'll see...
y' + 2y = 6x + 5 where y = 3x + 1
(3x + 1)' + 2(3x + 1) = 6x + 5
3 + 6x + 2 = 6x + 5
6x + 5 = 6x + 5 |
So that second guy only posted what he did to confuse me? What an annoying person. :wtf: |
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| starglider |
| quote: | Originally posted by DJ Cinos
So that second guy only posted what he did to confuse me? What an annoying person. :wtf: |
I don't know what the second guy did, but it doesn't seem to be how one would solve a differential equation. :nervous: |
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