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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

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

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