1. ranyai12

2. ranyai12

3. Spacelimbus

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

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

5. Spacelimbus

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

6. Spacelimbus

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

7. Spacelimbus

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

8. Spacelimbus

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

9. Spacelimbus

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

10. ranyai12

whats C?

11. Spacelimbus

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

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

13. Spacelimbus

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

14. Spacelimbus

no wait, C=1

15. ranyai12

ok let me check

16. Spacelimbus

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

since we have initial conditions.

18. ranyai12

it's wrong:(

19. Spacelimbus

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

20. Spacelimbus

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

21. ranyai12

ok let me check

22. ranyai12

it's wrong :(

23. Spacelimbus

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

24. ranyai12

yea but dont we stop there

25. Spacelimbus

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

26. ranyai12

yea thats what I got earlier and it was wrong

27. Spacelimbus

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

28. ranyai12

oh

29. Spacelimbus

So inverse that and you should get the solution

30. Spacelimbus

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

oh ok

32. Spacelimbus

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

33. ranyai12

I did the step and it ended up being wrong

34. ranyai12

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

35. Spacelimbus
36. ranyai12

yea that doesnt work

37. Spacelimbus

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

38. ranyai12

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

39. Spacelimbus

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

40. ranyai12

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

41. Spacelimbus
42. Spacelimbus

somewhere in my notes I have an error.

43. Spacelimbus

got that @ranyai12 ?

44. ranyai12

yea

45. Spacelimbus

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

46. ranyai12

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

yeh I will.

48. ranyai12

thank you!

49. Spacelimbus

no problem