_D_6 The set of critical points of the autonomous equation y' = y(2-y) are: A (0.2.-2)...
(4 pts) Solve the IVP xy,-2y + хуг, y(1) 0. a) y-0 (b) y 3-2 3r 8-3 (e) None of the above 4 pts) A tank has a capacity of 20 liters. Starting with 10 liters of pure water saltwater containing 50 grams/liter of salt is pumped into the tank at a rate of 2 liters per minute while the tank is kept thoroughly mixed and drained at 1 liters per minute. How much salt is in the tank when...
Find the function y=y(x) (for x>0) which satisfies the separable differential equation dy/dx = (4+17x)/(xy^2). ;x>0 with the initial condition: y(1)=2
please, write the necesery steps clearly, thank you. diidertial equation question #5 (1) What is the order of the following differential equation? y? + 6x*y" = sinº (2) Solve 16r2 -0. (3) Suppose Tank A initially has 30 gallons of water containing 55 ounces of dissolved salt, and Tank B initially has 20 gallons of water containing 26 ounces of dissolved salt. Water from an external source with a salt concentration of 1 ounce per gallon flows into Tank A...
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line. 4 Consider the autonomous differential equation y f(v)...
consider the autonomous equation 2. Consider the autonomous equation y=-(y2-6y-8) (a) Use the isocline method to sketch a direction field for the equation (b) Sketch the solution curves corresponding to the following intitial conditions: (1) y(0) 1 (2) y(0) =3 (3) y(0)=5 (4) 3y(0) 2 (5) y(0) = 4 (c) What are equilibrium solutions, and classify its equilibrium them as: sink (stable), source, node. (d) What is limy(t) if y(0) = 6? too 2. Consider the autonomous equation y=-(y2-6y-8) (a)...
2. (10 points) An aquarium has a 1000 L tank containing 400 L of salt water with a concentra- tion of 210 grams per liter. A salt water solution with a concentration of 470 grams per liter is pumped into the tank at a rate of 5 liters per minute. The well-mixed solution is drained from the tank at a rate of 3 liters per minute. Additionally, the tank is uncovered, so fresh water evaporates from the tank at a...
1. Solve the following homogeneous differential equation. ty' = 1. cos (6) + y 2. Solve the following Bernoulli differential equation 3. Solve the following initial value problem. (Hint: transform the equation to a separable equation through a substitution) y-(x + y + 1)? (0) - V3 - 1 4. Let T represent the temperature (in °F) of an object in a room whose temperature is kept at a constant 60°. If the object cools from 100 to 90° in...
e critical points for the autonomous equation y'=y (ay) e whether they lead to equilibrium solubions which are shable, unstable or semesbable equilíbria. A solue g =- Jy y (0)=50 X+goo o solve y + y = x 0 Prove that the equation cosy dx - (x sing-y dy=0 s excent and then solve. 2 Prove that the ogrubion (easing) dx+cos ydy=0 is nob excent and then find an anbegrubina factor which will make it exact. Prove that exy dx...
If z = xy + xf (?), then xgie + y + z = xy. O True O Falsem 11== f ($x + 2), then 29. – 3.3 -1. then O True False If z = , then x2 + y a = 2 True 0 False If w = f (xz, yz), then xy + y O True 0 False
(1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For each of the following functions g determine if the corresponding functionf is continuous on the whole plane. Use "T" for true,"F" for false 2. g(x, y) 9x2y 3. gx, y)-4 sin) 4. g(x, y) xy sin(xy) 5. g(x, y) 3xy (1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For...