Question

Can anyone help with LaPlace transforms?

Answer 1

y'’ + y = 1, y(0) = 1, y’(0) = 1

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

replace f's with y's right?

Answer 7

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