Question

$laplace\:e^{\frac{t}{2}}$

solve it

how to do it

Answer 1

$\mathrm{Laplace\:Transform\:of\:}e^{\frac{t}{2}}:\quad \frac{2}{2s-1}$

$L\left\{e^{\frac{t}{2}}\right\}$

$\mathrm{Use\:Laplace\:Transform\:table}:\quad \:L\left\{e^{at}\right\}=\frac{1}{s-a}$

$L\left\{e^{\frac{1}{2}t}\right\}=\frac{1}{s-\frac{1}{2}}$

$=\frac{1}{s-\frac{1}{2}}$

$=\frac{2}{2s-1}$

Answer 2

Answer:

I would like to use the Laplace transform symbol that appears in unicode (SCRIPT CAPITAL L U+2112)

Laplace Unicode

However, I could only find the following two symbols can be used for Laplace transforms:

mathcal and mathscr

There are other symbols provided by the math-unicode, but it seems that it does not work with pdflatex.