Problem 7. A Bernoulli equation is a particular kind of first order ODE that can be written in the form x'(t) = a(t)x+ g(t)x" where some integer n #1, and a(t) are some suitably integrable functions. Using the substitution y(x) = x¹-n, we can actually rewrite this equation as an ODE involving the dependent variable y instead. Use this technique to solve the initial value problem x' (t) = 2 2t -x+ 3t X x(1) = 2 Hint: when rewriting the equation using your substitution, you should find a way to use the substitution so that the variable x does not appear at all-it should only contain y and t as variables. Once you find a solution, you should reexpress it in terms ofx and t. "

please solve this with clear text, as the last solution was not clear, also with full detail as well

You are designing a poster which has a border around the printed portion. The border is 2 inches wide on the left and right sides, and 3 inches wide on the top and bottom. The entire poster will be a total of 300 square inches, including the borders and printed portion combined.