Just started an assignment and the first question was on Laplace Transforms. I tried to find a solution to the problem first by finding the general and particular solution . I did this as i haven't had a great deal to do with laplace and was seeing if i could find the solution useing methods i learnt last year (well suposed to have learnt) so i had an idea what the answer should look like as i attempted the question. Can someone please have a look over my work and tell me if my solution is correct (im not very confident with it).
Ok thanks alot for that Jhevon.
So i am looking for an answer that looks like y(t)=e^t-te^-4t. I will atempt the question useing laplace transforms tonight if you could take another look then? Thanks again for your help, I appreciate it.
Thank You very much for the offer but i will not hold you up. I attempted it roughly with laplace and after a short battle with partial fractions it came out the same supprisingly.
Thanks once again, It makes it so much easier haveing a place that people are willing to look over your working out.
Ps. now onto fourier serries, no doubt you guys will hear from me again.
I will write to mean
Now by the method of Partial Fractions:
By equating the coefficients of like powers of , we obtain the system of equations:
Solving this, we get:
And so we see,
by taking the inverse Laplace Transform...which is what you got before
I did the partial fractions in 2 parts, but i just looked at the question again and it says "Use partial fractions to invert this expression and find the solution y(t).". Does this mean that i should have done it the way you did.
my expression for Y(s)=
(-1/5)/(s+4) - 1/(s+4)^2 + (1/5)/(s-1) + (1/5)/(s+4) + (4/5)/(s-1)
answer comes out the same tho i am unsure about the "invert" in the question.
the invert part is just talking about the last step we did. that is, going from the partial fractions back to functions of t
Your way was alot shorter. It took me probally about half a page more to come up with the partial fractions because i did it in 2 parts and also used the other method (is it called the coverup method or something like that?). I will try practice the method you have used because it looks like it will save me a bit of time in the future.
Good luck with your class.