1. anonymous

2. anonymous

3. anonymous

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. anonymous

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

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. anonymous

whats C?

11. anonymous

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. anonymous

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

13. anonymous

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

14. anonymous

no wait, C=1

15. anonymous

ok let me check

16. anonymous

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. anonymous

since we have initial conditions.

18. anonymous

it's wrong:(

19. anonymous

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

20. anonymous

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

21. anonymous

ok let me check

22. anonymous

it's wrong :(

23. anonymous

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

24. anonymous

yea but dont we stop there

25. anonymous

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

26. anonymous

yea thats what I got earlier and it was wrong

27. anonymous

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

28. anonymous

oh

29. anonymous

So inverse that and you should get the solution

30. anonymous

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. anonymous

oh ok

32. anonymous

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

33. anonymous

I did the step and it ended up being wrong

34. anonymous

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

35. anonymous
36. anonymous

yea that doesnt work

37. anonymous

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

38. anonymous

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

39. anonymous

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

40. anonymous

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

41. anonymous
42. anonymous

somewhere in my notes I have an error.

43. anonymous

got that @ranyai12 ?

44. anonymous

yea

45. anonymous

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

46. anonymous

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. anonymous

yeh I will.

48. anonymous

thank you!

49. anonymous

no problem