It's because in the complimentary function it doesn't have a constant in front of it. It has Acos3x or Bsin3x in front of it. If the complimentary function was of the form Ae^-x +Be^-3x then yes you test xe^-x because both the CF's and PI's e^-x have a constant in front of it and nothing else.
It's because in the complimentary function it doesn't have a constant in front of it. It has Acos3x or Bsin3x in front of it. If the complimentary function was of the form Ae^-x +Be^-3x then yes you test xe^-x because both the CF's and PI's e^-x have a constant in front of it and nothing else.
It's because in the complimentary function it doesn't have a constant in front of it. It has Acos3x or Bsin3x in front of it. If the complimentary function was of the form Ae^-x +Be^-3x then yes you test xe^-x because both the CF's and PI's e^-x have a constant in front of it and nothing else.
If you expand the bracket into A(e^-x)sin(3x) + B(e^-x)cos(3x) doesn't that makes it "have a constant in front of it" ?
You can't use e^-x for the PI because it is an invalid solution. You would get 9 = 27 essentially. If you make the the PI y = ke^x you get a valid solution. ke^x wouldn't work IF it gave LHS = 0. This would be invalid because you can't have a solution that satisfies LHS = 0 and LHS = 27e^x at the same time. Only in this situation would you use y = kxe^-x
You can't use e^-x for the PI because it is an invalid solution. You would get 9 = 27 essentially. If you make the the PI y = ke^x you get a valid solution. ke^x wouldn't work IF it gave LHS = 0. This would be invalid because you can't have a solution that satisfies LHS = 0 and LHS = 27e^x at the same time. Only in this situation would you use y = kxe^-x
(I used k as a constant)
You might wanna rephrase your answer because I don't think i understand what you're saying
This is a bit unrelated to the thread but is there a way to remove the UCAS clearing pop-up notification? It comes up every time I refresh or click through a few pages. It's quite annoying ^^
But it also has sin3x or cos3x attached to it. It's not Ae^-x on its own.
Just had a thought because no matter how much you differentiate A(e^-x)sin(3x) + B(e^-x)cos(3x) it'd always be a product of 2 functions, never a function of e by itself, which was the explanation i needed...
This is a bit unrelated to the thread but is there a way to remove the UCAS clearing pop-up notification? It comes up every time I refresh or click through a few pages. It's quite annoying ^^
Just had a thought because no matter how much you differentiate A(e^-x)sin(3x) + B(e^-x)cos(3x) it'd always be a product of 2 functions, never a function of e by itself, which was the explanation i needed...