Please all the work!! Solve by Laplace transform: y"-3y'+2y = e^(3x)  and y(0)=1,y'(0)=0

Find the inverse Laplace transform of F(s)=(s−2)/(s^2−7s+12) f(t) =

Solve for the Laplace Transform1. y(t) = 5e^(-2t) cos6t2. f(t) = 3e^(-4t) (1 -3t +2t^23. f(t) = (2(3t-5)^2) / (e^4t)

Find laplace transform of x" + 3x' + 2x = t(e^(-t)) Where x'(0) = 0 , x(0) = 1

Sole by Laplace Transform: y''-4y=4t-8e^(-3t);  y(0)=0, y'(0)=1

dy/dx + y = xy^3   Solve the Bernoulli equation using v=y^(1-n) transform

Find the inverse Laplace transform, f(t) of the function F(s)=6s^(−3/2), s>0f(t)=    t>0

find the laplace transform of the function f(t)=e^-t (cos 4t - 2sin 4t)

please solve if needed with using v=y^(1-n) transform

find the inverse Laplace transform of the given function of 4e^(-2t) / (s(s+4))   Thank you for the help.