chelseacowper
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On the jan 2005 paper, I don't understand why on the mark scheme for Question 6(b) it just says "may just write it down". I don't get why that equation is used (v=Asin3x + Bcos3x) because completing part (a) gives you an auxiliary equation of "u^2 + 9 =0" which doesn't fit into any if the complimentary function formulas. Why do you use the particular integral trial solution, if that is what is actually being used as that's the only think I can seem to link it to, that includes sinx and cosx?

If you understand this (I've tried my best to explain haha) will someone please help me?
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brianeverit
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(Original post by chelseacowper)
On the jan 2005 paper, I don't understand why on the mark scheme for Question 6(b) it just says "may just write it down". I don't get why that equation is used (v=Asin3x + Bcos3x) because completing part (a) gives you an auxiliary equation of "u^2 + 9 =0" which doesn't fit into any if the complimentary function formulas. Why do you use the particular integral trial solution, if that is what is actually being used as that's the only think I can seem to link it to, that includes sinx and cosx?

If you understand this (I've tried my best to explain haha) will someone please help me?
If the roots of the auxilliary equation atre complex, i.e. p\pm q\text{j} then the complementary function is \text{e}^{px}(A\sin qx+B\cos qx) so it follows that if the auxilliary equation has roots \pm3\text{j} then the C.F. is  A\sin3x+B\cos3x since p=0\implies\text{e}^{px}=1
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chelseacowper
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Thank you that's make soooo much more sense
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