please help, thanks its blured a bit but it says y g/L Consider the initial value...
(1 point) A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt per liter enters a tank at the rate 7 L/min. The solution is mixed and drains from the tank at the same rate. (a) What is the concentration of our solution in the tank initially? concentration = !!! (kg/L) (b) Set up an initial value problem for the quantity y, in kg, of salt in the tank...
Solve the differential equation. 7) dy Y-(In x5 7) dx х Solve the initial value problem. 8) e dy + y = cos e; e > 0, y(n) = 1 de 8) Solve the problem. 9) A tank initially contains 120 gal of brine in which 50 lb of salt are dissolved. A brine containing 1 lb/gal of salt runs into the tank at the rate of 10 gal/min. The mixture is kept uniform by stirring and flows out of...
Previous Problem Problem List Next Problem (1 point) A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 6 L/min. (a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes: !!! (kg/min) y(0) = 60 !!! kg (b) Solve the initial value problem in part (a) y(t)...
(2 pts) A 150 L tank contains 100 L of pure water. Brine that contains 0.1 kg of salt/L enters the tank at 5 L/min. The solution is kept thoroughly mixed and drains from the tank at the rate of 4 L/min. Find the concentration of the salt in the tank at the moment it is full. (2 pts) Separate variables and use partial fractions to solve the following initial value problem. da T = x (- 1), x(0) =...
I just need help understand
where I get the 7 for the dx/dt
1. (5 points) Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from Tank A into Tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into Tank A...
(1 point) Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 10 L (liters) of water and 355 g of salt, while tank 2 initially contains 90 L of water and 345 g of salt. Water containing 40 g/L of salt is poured into tank1 at a rate of 4 L/min while the mixture flowing into tank 2 contains a salt concentration of 20 g/L of salt and is flowing at the rate of 1...
Differential Questions problem. Can someone help. Thanks.
1. Consider the initial valuc problenm ay + 5y-cost, y(0) = 1. Solve the IVP using THREE DIFFERENT METHODS. 2. Solve the following differential equations. If there are initial values, solve the IVP. If there are not, find the general solution. (a) (2x + y)dr + (Zy +エ)dy = 0, y(2) =-3; (o) du) dx 2y +4y 3. Solve the following initial value problems y" + 2/ + 5y = 0, y(0) =-1,...
Please solve this in Matlab
Consider the initial value problem dx -2x+y dt x(0) m, y(0) = = n. dy = -y dt 1. Draw a direction field for the system. 2. Determine the type of the equilibrium point at the origin 3. Use dsolve to solve the IVP in terms of mand n 4. Find all straight-line solutions 5. Plot the straight-line solutions together with the solutions with initial conditions (m, n) = (2, 1), (1,-2), 2,2), (-2,0)
please help with entire question
7(0) = -5. Consider the initial value problem 47" + 28y' +49-0, (0) - 1, (a) Solve the initial value problem. X(t) Plot its solution for osts 5. (A computer algebra system is recommended.) (b) Determine where the solution has the value zero. (c) Determine the coordinates (to, Yo) of the minimum point. (to yo)-( (d) Change the second initial condition to y(0) -b and find the solution as a function of b. Xt) Find...
Please help both questions, thanks
(1 point) Let g(t) = e2 a Solve the initial value problem 4 – 2 = g(t), using the technique of integrating factors. (Do not use Laplace transforms.) y(0) = 0, (t) = b. Use Laplace transforms to determine the transfer function (t) given the initial value problem 6' - 24 = 8(t), (0) = 0. $(t) = c. Evaluate the convolution integral (6 + 9)(t) = Sølt – w)g(w) dw, and compare the resulting...