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

Question

anonymous · Answer

http://en.wikipedia.org/wiki/Method_of_undetermined_coefficients

anonymous · Answer

give me the equation

anonymous · Answer

ok( D^2-5D+6)y=e^3x+sinx

anonymous · Answer

just tell me the assumed particular integral.....

anonymous · Answer

bad diff equation, what is D?

anonymous · Answer

D is the notation for operator d/dx....

anonymous · Answer

$$y^{\prime\prime}-5y^\prime+6y=\operatorname{e}^{3x}+\sin x$$

anonymous · Answer

yeah

anonymous · Answer

I think one of the best ways to solve this equation is by using Laplace transformation

anonymous · Answer

in the question it is specifically mentioned to use method of undetermined coefficients

anonymous · Answer

The particular solution will be the sum of particular solutions.  Try Ae^(3x) + Bsin(x)

anonymous · Answer

solve for A and B

anonymous · Answer

no it will not work as e^3x is a term in complementary function

anonymous · Answer

particular solution $$y=Ae^{\lambda1 x}+Be^{\lambda2 x}$$, lambda are complex numbers

anonymous · Answer

yeah...i just did it and it's a mess...too much to write out...buggin' out and going to bed...good luck.

anonymous · Answer

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,$$y_p=Axe^{3x}+M \sin x +N \sin x$$

anonymous · Answer

I think I ended up with A=1, M=N=(1/10).  Try it.

anonymous · Answer

$$C _{1} e^{2x} + C_{2}e^{3x} +0.1(\cos[x] + \sin[x])+xe^{3x}$$

anonymous · Answer

Yes

anonymous · Answer

thanx i ended up with the same solution guess the answer in the book was wrong