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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

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# I Laplace transform using differential equations

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