## anonymous 5 years ago Can anyone help with LaPlace transforms?

1. anonymous

y'’ + y = 1, y(0) = 1, y’(0) = 1

2. nikvist

$y''+y=1,y(0)=1,y'(0)=1$ $L(y''+y)=L(1)$ $s^2Y(s)-sy(0)-y'(0)+Y(s)=\frac{1}{s}$ $(s^2+1)Y(s)=s+1+1/s,Y(s)=\frac{s+1+1/s}{s^2+1}$ $Y(s)=\frac{s^2+s+1}{s(s^2+1)}=\frac{1}{s}+\frac{1}{s^2+1}$ $L^{-1}(Y(s))=1+\sin{x}$

3. anonymous

Hmm ok lemme see what it looks like compared to mine.

4. anonymous

The second step if you were to write it all out would look like this right?$s^2L(y)-s f(0)-f(0)-L(y)=L(1)$

5. nikvist

correct is $s^2L(y)-sy(0)-y'(0)+L(y)=L(1)$

6. anonymous

replace f's with y's right?

7. anonymous

We're saying the same thing I'm using f's