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## anonymous 5 years ago can anyone say how to solve a differential equation using method of undetermined coefficients??

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1. anonymous
2. anonymous

give me the equation

3. anonymous

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

4. anonymous

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

5. anonymous

bad diff equation, what is D?

6. anonymous

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

7. anonymous

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

8. anonymous

yeah

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

solve for A and B

13. anonymous

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

14. anonymous

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

15. anonymous

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

16. anonymous

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

17. anonymous

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

18. anonymous

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

19. anonymous

Yes

20. anonymous

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

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