Using the Laplace transform and showing the details of your work, solve the IVP: 8. y₁= -2y+3y2, y2 = 4y1 - y2 y1(0) = 4, y₂(0) = 3

The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?

Solve the problem using Laplace transform

writing the given quadratic s^2 +6s + 10 in the form (s+a)^2 + B^2 (that is to complete the square).  I then want to compute the inverse Laplace transform of the function   (s+1) / (s^2+6s+10). Thank you so much for the help.