Laplace transform of \(\displaystyle{f{{\left({t}^{{2}}\right)}}}\) Suppose we know the

Find $L\{9+6t\}$
$L\left\{k\right\}=\frac{k}{s}$
$L\left\{t\right\}=\frac{1}{s^2}$

You drink a Starbucks Coffee in SM Seaside with a 120 mg. of caffeine. Each hour, the caffeine in your body system reduces by about 12 percent. How long will you have a 10 mg. of caffeine?

Use Laplace transforms to solve the following initial value problem
$y"-y^{\prime }-6y=0$
$y(0)=1$
$y^{\prime }(0)=-1$

Find the Laplace transform $L\{u_3(t)(t^2-5t+6)\}$
$a)F(s)=e^{-3s}(\frac{2}{s^4}-\frac{5}{s^3}+\frac{6}{s^2})$
$b)F(s)=e^{-3s}(\frac{2}{s^3}-\frac{5}{s^2}+\frac{6}{s})$
$c)F(s)=e^{-3s}\frac{2+s}{s^4}$
$d)F(s)=e^{-3s}\frac{2+s}{s^3}$
$e)F(s)=e^{-3s}\frac{2-11s+30s^2}{s^3}$

Find the differntial of each function.
a) ${\displaystyle y=\tan \sqrt{7t}}$
b) ${\displaystyle y=\frac{3-v^2}{3+v^2}}$

Solve the ff Differential equations. Indicate the type of differential equation
${\displaystyle y\ln x\ln ydx+dy=0}$

The Laplace transform of ${\displaystyle u(t-2)}$ is
(a) ${\displaystyle \frac{1}{s}+2}$
(b) ${\displaystyle \frac{1}{s}-2}$
(c) ${\displaystyle e^2\frac{s}{s}\left(d\right)\frac{e^{-2s}}{s}}$