If it is exact find a function F(x,y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation: (2x4 - 3y)dx + (-1x + 4y¹)dy = 0 First: My(x, y) = , and Nx (x, y) = If the equation is not exact, enter not exact, otherwise enter in F(x, y) here

Consider the function of two variables  u (x,t) = 2e-t sin (2x)  Select the option that gives a partial differential equation for which this function of two variables is a solution.  A. (∂2u/∂x2) = 4(∂2u/∂t2)  B. (∂2u/∂x2) = (1/4)(∂2u/∂t2)  C. (∂2u/∂x2) = - (1/4)(∂2u/∂t2)  D. (∂2u/∂x2) = -4 (∂u/∂t)  E. (∂2u/∂x2) = 4 (∂u/∂t)

The population of fish in a lake grows logistically according to the differential equation where t is in years with no harvesting. If the lake has 550 fish and opens to fishing, determine how many fish can be harvested per year to maintain equilibrium. dy/dt=0.1y(1-y/2500) Differential Equations

Consider the differential equation: dy/dx = y(3 - y) 1) Use the slope field plotter to plot different solutions corresponding to A: (0,-2); B: (0,1); C: (0,3); D: (0,4). You can drag each point to the correct place if they're somewhere else on the plane, or click on the point and redefine. Capture a screenshot showing all the solution curves and insert below. f'(x)=y(3-y) Kin/5 -5 Density Length dy de -8 Step size 0.1 Ymas y (3-9) Input. ✔Solution A Solution B Solution C Solution D DCQ= AC: 2) To what value does y(x) approach, as x → ∞, for the solutions corresponding to B,C, and D? To what value does y(x) approach, as x →∞, for the solution corresponding to A? Why is it different from the others? Be specific and answer in terms of what you know about the slope field and its effect on the solution. - 3) Use wolframalpha.com or something similar to find the particular solution corresponding to each of the points A,B,C,D. How is the solution through Point C different from the other…