can anyone say how to solve a differential equation using method of undetermined coefficients??

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can anyone say how to solve a differential equation using method of undetermined coefficients??

Mathematics
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http://en.wikipedia.org/wiki/Method_of_undetermined_coefficients
give me the equation
ok( D^2-5D+6)y=e^3x+sinx

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Other answers:

just tell me the assumed particular integral.....
bad diff equation, what is D?
D is the notation for operator d/dx....
\[y^{\prime\prime}-5y^\prime+6y=\operatorname{e}^{3x}+\sin x\]
yeah
I think one of the best ways to solve this equation is by using Laplace transformation
in the question it is specifically mentioned to use method of undetermined coefficients
The particular solution will be the sum of particular solutions. Try Ae^(3x) + Bsin(x)
solve for A and B
no it will not work as e^3x is a term in complementary function
particular solution \[y=Ae^{\lambda1 x}+Be^{\lambda2 x}\], lambda are complex numbers
yeah...i just did it and it's a mess...too much to write out...buggin' out and going to bed...good luck.
I thought the others were going to help you. Since e^(3x) is part of the homogeneous solution, try xAe^(3x) as one part. Since you have a trig. function too, add to this Msin(x) + Ncos(x). So try,\[y_p=Axe^{3x}+M \sin x +N \sin x\]
I think I ended up with A=1, M=N=(1/10). Try it.
\[C _{1} e^{2x} + C_{2}e^{3x} +0.1(\cos[x] + \sin[x])+xe^{3x}\]
Yes
thanx i ended up with the same solution guess the answer in the book was wrong

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