# Thread: How do I solve this Laplace Transform?

1. ## 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.

2. 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.

3. ## 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.

4. 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.

5. 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.

6. 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.