## ranyai12 Group Title Can Someone Please Help! (problem is attached) 2 years ago 2 years ago

1. ranyai12 Group Title

2. ranyai12 Group Title

3. Spacelimbus Group Title

hmm I don't have much practice with these, but if I am not completely mistaken then you have to find a general solution first and then a special solution?

4. Spacelimbus Group Title

General solution means, solving the homogenous differential equation, setting $$g(x)=0$$

5. Spacelimbus Group Title

To find $$g(x)$$ you can just take the inverse of the right hand side.

6. Spacelimbus Group Title

Can you check one answer? $\Large e^{-3t}+xe^{-3t}+e^{-t}-e^{-6t}+C$ C not yet calculated.

7. Spacelimbus Group Title

if none of that is correct, then I wouldn't know how to get this problem right, because of the delta function.

8. Spacelimbus Group Title

my guess is that only the first two are right, given by the homogenous system.

9. Spacelimbus Group Title

A few adds here for the right hand side $\Large \mathcal{L}_t \lbrace \delta(t-1) \rbrace(s)=e^{-s}$

10. ranyai12 Group Title

whats C?

11. Spacelimbus Group Title

a constant, haven't solved, but I am at doubt that the solution is correct for the third and the fourth term in general.

12. ranyai12 Group Title

you cant get partial credit so I can only check it at the end

13. Spacelimbus Group Title

hehe I actually get C=0 for the one above, so something looks dodgy

14. Spacelimbus Group Title

no wait, C=1

15. ranyai12 Group Title

ok let me check

16. Spacelimbus Group Title

If that doesn't work, I believe we have to do it step by step and can't separate it, which will be more work but should work.

17. Spacelimbus Group Title

since we have initial conditions.

18. ranyai12 Group Title

it's wrong:(

19. Spacelimbus Group Title

did you correct the x? Of course it should be there (-:

20. Spacelimbus Group Title

the other solution I got was this one $\Large 16te^{-3t}+e^{-t}-e^{-6t}$

21. ranyai12 Group Title

ok let me check

22. ranyai12 Group Title

it's wrong :(

23. Spacelimbus Group Title

Did you come to this point @ranyai12 ? $\Large Y=\frac{e^{-t}-e^{-6t}+16}{(s+3)^2}$

24. ranyai12 Group Title

yea but dont we stop there

25. Spacelimbus Group Title

$\Large Y= \frac{e^{-s}}{(s+3)^2}- \frac{e^{-6s}}{(s+3)^2}+ \frac{16}{(s+3)^2}$

26. ranyai12 Group Title

yea thats what I got earlier and it was wrong

27. Spacelimbus Group Title

That's not the solution we've got to inverse it.

28. ranyai12 Group Title

oh

29. Spacelimbus Group Title

So inverse that and you should get the solution

30. Spacelimbus Group Title

It's a step side function, from what I think, which would make sense too, I made a mistake earlier by keeping the time domain.

31. ranyai12 Group Title

oh ok

32. Spacelimbus Group Title

try that and then please tell me if it's correct.

33. ranyai12 Group Title

I did the step and it ended up being wrong

34. ranyai12 Group Title

i ended up getting (e^(-3t))(-e^(18)(t-6)step(t-6)+e^(3)(t-1)step(t-1)+16t)

35. Spacelimbus Group Title
36. ranyai12 Group Title

yea that doesnt work

37. Spacelimbus Group Title

I was checking on a similar problem and they attempt the problem the exact same way as we do.

38. ranyai12 Group Title

i know thats what confused me! I did it twice and got the same asnwer

39. Spacelimbus Group Title

can your program read it? Or do you need to substitute something for the stepside function ??

40. ranyai12 Group Title

i only have to substitute the theta to the wrod stepwhich i did and it was still wrong

41. Spacelimbus Group Title
42. Spacelimbus Group Title

somewhere in my notes I have an error.

43. Spacelimbus Group Title

got that @ranyai12 ?

44. ranyai12 Group Title

yea

45. Spacelimbus Group Title

We are only two constants off but I can't see where I have made the algebraic error yet.

46. ranyai12 Group Title

I ran out of tries anyway but thanks though and if you figure it out please let me knoe because it's killing me!

47. Spacelimbus Group Title

yeh I will.

48. ranyai12 Group Title

thank you!

49. Spacelimbus Group Title

no problem