# Partial differential equation-delta Dirac& Heaviside function!

I got 2 questions to ask! I have finished one but not sure if it's correct so I need to double check with someone :)

http://imageshack.us/a/img708/1324/83u8.png [Broken]

Here is my worked solution, I took this picture with my S4 and I wrote is very neatly as I could! The reason I didn't type it all out since the maths is too much, so I'm sorry ): Question 2 answer: http://img23.imageshack.us/img23/134/8knw.jpg [Broken]

and http://img202.imageshack.us/img202/1538/klg5.jpg [Broken] If you are wondering what graph I'm talking about, here it is: http://img16.imageshack.us/img16/4435/s2yd.png [Broken]

For the 3 question, I gave it a try but I'm sure it's wrong so if you could solve it for me. It is very nice of you! I know it's in this form t^2 [H(t-3)-H(t-4)] Thank you for taking your time to help me! Cheers

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rude man
Homework Helper
Gold Member
Did you cover the Laplace transform?

Did you cover the Laplace transform?
Yes, I did. Sometime its hard to rearrange function for inverse lagrange.
I managed to work out the solution for question 3. So could you or someone check my question 2 please!

rude man
Homework Helper
Gold Member
EDIT: I need to correct a typo:

Don't go e-sT = 1/esT. T a constant, in your case 10 and 30.
Any F(s)e-sT inverses to f(t-T)U(t-T) where F(s) inverses to f(t) (shifting theorem). Use that fact whenever you get an e-sT coefficient in the s domain.

Your original transformed equation is correct.

I wouldn't try partial fraction expansion with an esT term in the original F(s). Do your p/f expansion with the polynomial expression only, then use the shifting theorem.

OK, I looked at your solution. I got 2/5 instead of 4/5 for the sin(t-10) term. I might as well confess I used Wolfram Alpha.

But the main problem was whenver you had an exp term you wrote e-at instead of e-a(t-T).

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Don't go e-sT = 1/esT. T a constant, in your case 10 and 30.
Any F(s)e-sT inverses to f(t)U(t-T) where F(s) inverses to f(t) (shifting theorem). Use that fact whenever you get an e-sT coefficient in the s domain.

Your original transformed equation is correct.

I wouldn't try partial fraction expansion with an esT term in the original F(s). Do your p/f expansion with the polynomial expression only, then use the shifting theorem.
Well I know the Laplace you are talking about, I was using it for question 1.
For an example 3/(s+3)^3
Y(t)= 3/2 t^2 e^-3t
I usually do the algebra way but this question is too hairy so that's why I'm not sure if my working out is correct so if you could work your way and compare to my answer see you would get the same?

My teacher do this method but I'm not sure if its right though
1/s e^10s (s^2+4s+5)
=1/5 [(1/s -s+2/(s+2)^2+1 -2/(s+2)^2+1 ]e^-10s

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rude man
Homework Helper
Gold Member
PS why did you call this thread "partial" differential equation?

PPS look again at my post #4.

PS why did you call this thread "partial" differential equation?

PPS look again at my post #4.
Well... that's the name of the math course I'm doing so yeah
I think my p/f is wrong and my teacher way is right
1/s e^10s (s^2+4s+5)
transform to and then you just look up the table
=1/5 [(1/s -s+2/(s+2)^2+1 -2/(s+2)^2+1 ]e^-10s

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