## ChmE Group Title Method of undetermined coefficients... one year ago one year ago

1. ChmE Group Title

Must be in the form$ay''+by'+cy=Ct ^{m}e ^{rt}$What does C stand for? I thought it was a constant but the equation$y''+2y'-y=t ^{-1}e ^{t}$Does not satisfy this method. i assumed C=1 so it would, bu tit doesn't. Explanation?

2. ChmE Group Title

@UnkleRhaukus

3. ChmE Group Title

Find a particular solution to the differential equation$4y''+11y'-3y=-2te ^{-3t}$

4. across Group Title

I believe that the method only applies for $$m\geq0$$, but I cannot recall to save my life.

5. ChmE Group Title

$4r ^{2}+11r-3=0\rightarrow (4r-1)(r+3)\rightarrow r= \frac{ 1 }{ 4 },-3$

6. ChmE Group Title

That makes sense I'm going to look that up. Thanks

7. ChmE Group Title

@across I found it you are right

8. ChmE Group Title

since -3 does appear as a root s=1 which is the multiplicity of the root -3

9. ChmE Group Title

Ok @UnkleRhaukus I could use a little help on my last problem of the night. I posted the question in this stream 3rd from the top.

10. ChmE Group Title

$Y _{p}= t(Ae ^{-3t})$Do I have to include the other root as well?

11. ChmE Group Title

@Directrix @Hero Can I have a little push in the right direction

12. ChmE Group Title

@Hero do you see a mistake I have made or is anything coming to you about what to do next?

13. Hero Group Title

Sorry, I'm busy doing my own work at the moment.

14. ChmE Group Title

The answer in the back of the book is $(\frac{ t }{ 13 }-\frac{ 8 }{ 169 })te ^{-3t}$

15. ChmE Group Title

Oh, I understand

16. ChmE Group Title

@satellite73 @.Sam.

17. ChmE Group Title

@UnkleRhaukus Just in time I was about to give up. Do you mind helping me with this last question?

18. UnkleRhaukus Group Title

where are you up to

19. ChmE Group Title

I feel like I need to plug in $Y _{p},Y'_{p}, Y''_{p}$into the original to solve for A. I am up to writing an equation for Yp

20. ChmE Group Title

I feel like I have my roots and s correct

21. UnkleRhaukus Group Title

$4y''+11y'-3y=-2te ^{-3t}$ $4r^2+11r-3=0$$(4r-1)(r+3)=0$$r=1/4,-3$ $y_c=ae^{t/4}+be^{-3t}$

22. ChmE Group Title

Oh ya I forgot, when you have two diff roots you need to use two different unknowns. What about the t^s? My teacher threatened us if we forgot that on the test

23. ChmE Group Title

As i understand it t^s, where s is the multiplicity of your roots needs to be out in front.

24. UnkleRhaukus Group Title

$y_p=t\left(c\cdot e^{-3t}+d\cdot t\cdot e^{-3t}\right)$

25. ChmE Group Title

Why do you have two terms in the ( ) if m=1 shouldn't there be 1. And I don't mean to come across like I'm questioning you, just trying to undersstand

26. UnkleRhaukus Group Title

its a second order equation there will be two solutions

27. ChmE Group Title

So I see your Yp matches the books except I need to now solve for c and d by plugging Yp into the original equation right?.........Ok

28. UnkleRhaukus Group Title

take the first and second derivative of y_p

29. ChmE Group Title

Right then plug it in. I can do that on my own later. Thanks for your help again. I'm calling it a night

30. UnkleRhaukus Group Title

see you next time