How do I solve this Laplace Transform?

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April 28th 2009, 03:01 AM
LooNiE

How do I solve this Laplace Transform?

The equation I have is 3(dy/dx) + 4y = 4 +6x + 4x^2
I am given that y = 1 when x = 0.
Basically, I can do the initial transform, but afterwards I get completely cnofused. Any help is appreciated.
April 28th 2009, 03:11 AM
mr fantastic

Quote:

Originally Posted by LooNiE

The equation I have is 3(dy/dx) + 4y = 4 +6x + 4x^2
I am given that y = 1 when x = 0.
Basically, I can do the initial transform, but afterwards I get completely cnofused. Any help is appreciated.

Please post what you've done and where you got stuck.
April 28th 2009, 03:46 AM
LooNiE

what i've done

Ok what I have done is take L.T's, which gives me this:

dont know what the symbol here is but its always Y bar

3(sy - 1) +4y = 4/s + 6/s^2 + 8/s^3

So then I get:

y(3s + 4) = 4/s + 6/s^2 + 8/s^3 + 3

I dont know how to proceed from here. I could obviously divide the rand hand side by (3s+4) but im not completely certain if I need to do anything else first.
April 28th 2009, 03:50 AM
mr fantastic

Quote:

Originally Posted by LooNiE

Ok what I have done is take L.T's, which gives me this:

dont know what the symbol here is but its always Y bar

3(sy - 1) +4y = 4/s + 6/s^2 + 8/s^3

So then I get:

y(3s + 4) = 4/s + 6/s^2 + 8/s^3 + 3

I dont know how to proceed from here. I could obviously divide the rand hand side by (3s+4) but im not completely certain if I need to do anything else first.

Do divide. Then express each term on the right hand side in partial fraction form. Then look up your tables to get the corresponding inverse Laplace transforms.

Check your answer by confirming that it satisfies the DE and confirming that y(0) = 1.
April 28th 2009, 04:04 AM
LooNiE

If I divide on the right hand side, they are all already in partial fracion form. From my teacher, I know that the answer is y = 1 + x^2, but I dont see how I can get the answer from what I have.
April 28th 2009, 04:30 AM
mr fantastic

Quote:

Originally Posted by LooNiE

If I divide on the right hand side, they are all already in partial fracion form. From my teacher, I know that the answer is y = 1 + x^2, but I dont see how I can get the answer from what I have.

$\frac{4}{s (3s + 4)}$ etc. are not in partial fraction form. eg. The partial fraction form of $\frac{4}{s (3s + 4)}$ is $\frac{A}{s} + \frac{B}{3s + 4}$ where you have to find the value of A and B.