Find the function y = y() (for a > 0) which satisfies the separable differential equation dy 4 + 14x x > 0 dx xy2 with the initial condition y(1) = 4.a E Solve the separable differential equation _y dt t2y+y' Use the following initial condition: y(0) = 3. Write answer as a formula in the variable t. Suppose that a population grows according to the unlimited growth model described by the d differential equation 5127: = 0.23; and we are given the initial condition 31(0) = 350. Find the size of the population at time t = 5. (Okay to round your answer to closest whole nl Imhnr \\ Let y(t) represent your bank account balance, in dollars, after t years. Suppose you start with $70000 in the account. Each year the account earns 4% interest, and you deposit $9000 into the account. This can be modeled with the differential equation: _ 0 04y + 9000 _9_ dt y(0 )= 70000 Solve this differential equation for y(t) V(t)=' \\ Ionsider the differential equation 31' = y w A) At the point (0.5, 1), the direction field has a slope of B) At the point (1.5, 1), the direction field has a slope of C) Along the x-axis the slope of the direction field is equal to which number or expressio E D) Along the y-axis the slope of the direction field is equal to which number or expressio 1 x E) Use your answers above to help choose the correct direction field for the differential equation. (y 4)2(y2 + 7y + 10) 1 20 lllll .1 Below is the slope field of y' is 3 3 i % What are the equilibrium solutions for this differential equations? Give your answers from smallest to largest. 8/1 1/1 3/2 = 93 = Classify each equilibrium solution as stable, unstable, or semi-stable. Suppose that a population grows according to the unlimited growth model described by the d differential equation 61: = 0.23; and we are given the initial condition 31(0) = 350. Find the size of the population at time t = 5. (Okay to round your answer to closest whole number.)