Laplace transform using differential equations

[Belgium 12]

Hi members,

Laplace transform using differential equations.(see attached PDF file)

My question d/ds(s^2 y- s Y(0)-Y'(0).)...
Y(t)=sin(sqrt(t)) Y(o)=0
Now Y'= cos(sqrt(t)/2sqrt(t) Y'(0)=infinity

d/ds (Y'(0)=?? can it be treated as a constant or can we change limit and differentiation??I don't think so.
like d/ds (cos(sqrt(t))/2sqrt(t)=0

Thank you

 

[Mark44]

Hi members,

Laplace transform using differential equations.(see attached PDF file)

My question d/ds(s^2 y- s Y(0)-Y'(0).)...
Y(t)=sin(sqrt(t)) Y(o)=0
Now Y'= cos(sqrt(t)/2sqrt(t) Y'(0)=infinity

d/ds (Y'(0)=??

Y(0) and Y'(0) are constants, so their derivatives are both zero.

can it be treated as a constant or can we change limit and differentiation??I don't think so.
like d/ds (cos(sqrt(t))/2sqrt(t)=0

Thank you

 

[Belgium 12]

Hello Mark 44,

If I understand it,Y'(0)=infinity.Here infinity can be treated as a constant.

Thank you