Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

Can Someone Please Help! (problem is attached)

MIT 18.03SC Differential Equations
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SIGN UP FOR FREE
1 Attachment
@Spacelimbus Please help! I know I asked you before but good news is I figured the other one out! so, if you can please help!
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?

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

General solution means, solving the homogenous differential equation, setting \(g(x)=0 \)
To find \(g(x)\) you can just take the inverse of the right hand side.
Can you check one answer? \[\Large e^{-3t}+xe^{-3t}+e^{-t}-e^{-6t}+C \] C not yet calculated.
if none of that is correct, then I wouldn't know how to get this problem right, because of the delta function.
my guess is that only the first two are right, given by the homogenous system.
A few adds here for the right hand side \[\Large \mathcal{L}_t \lbrace \delta(t-1) \rbrace(s)=e^{-s} \]
whats C?
a constant, haven't solved, but I am at doubt that the solution is correct for the third and the fourth term in general.
you cant get partial credit so I can only check it at the end
hehe I actually get C=0 for the one above, so something looks dodgy
no wait, C=1
ok let me check
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.
since we have initial conditions.
it's wrong:(
did you correct the x? Of course it should be there (-:
the other solution I got was this one \[\Large 16te^{-3t}+e^{-t}-e^{-6t} \]
ok let me check
it's wrong :(
Did you come to this point @ranyai12 ? \[\Large Y=\frac{e^{-t}-e^{-6t}+16}{(s+3)^2} \]
yea but dont we stop there
\[\Large Y= \frac{e^{-s}}{(s+3)^2}- \frac{e^{-6s}}{(s+3)^2}+ \frac{16}{(s+3)^2} \]
yea thats what I got earlier and it was wrong
That's not the solution we've got to inverse it.
oh
So inverse that and you should get the solution
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.
oh ok
try that and then please tell me if it's correct.
I did the step and it ended up being wrong
i ended up getting (e^(-3t))(-e^(18)(t-6)step(t-6)+e^(3)(t-1)step(t-1)+16t)
http://www.wolframalpha.com/input/?i=laplace+transform+%28e%5E-s%29%2F%28s%2B3%29%5E2%29-+%28e%5E%28-6s%29%29%2F%28s%2B3%29%5E2%2B%2816%29%2F%28s%2B3%29%5E2
yea that doesnt work
I was checking on a similar problem and they attempt the problem the exact same way as we do.
i know thats what confused me! I did it twice and got the same asnwer
can your program read it? Or do you need to substitute something for the stepside function ??
i only have to substitute the theta to the wrod stepwhich i did and it was still wrong
http://www.wolframalpha.com/input/?i=x%27%27%2B6x%27%2B9x%3Ddelta%28t-1%29-delta%28t-6%29%2Cwith+x%280%29%3D2+and+x%27%280%29%3D2
somewhere in my notes I have an error.
got that @ranyai12 ?
yea
We are only two constants off but I can't see where I have made the algebraic error yet.
I ran out of tries anyway but thanks though and if you figure it out please let me knoe because it's killing me!
yeh I will.
thank you!
no problem

Not the answer you are looking for?

Search for more explanations.

Ask your own question