Question

inverse laplase

Answer 1

\[\frac{ 2s-5 }{ s ^{2} -4s +13 }\]

Answer 2

can you factor the denominator using 'completing the square' method

Answer 3

i have done the completing the square
(s-2)+9

Answer 4

dont forget the ^2

Answer 5

sorry i forgot about that....
then i dont know the next step

Answer 6

something like this
\[(s-2)^2+3^2\]

Answer 7

so we have
\[\mathcal L^{-1}\left\{\frac{ 2s-5 }{ s ^{2} -4s +13 }\right\}\]
\[=\mathcal L^{-1}\left\{\frac{ 2s}{ (s-2)^2+3^2} -\frac{5 }{ (s-2)^2+3^2 }\right\}\]

now apply the shift theorem

Answer 8

for 2s/(s-2)^2+9
whish teorem i shpuld appllied

Answer 9

Shift theorem\[\large\boxed{\mathcal L^{-1}\left\{F(s+a)\right\}=e^{-at}\mathcal L^{-1}\left\{F(s)\right\}=e^{−at}f(t)}\]

Answer 10

?????