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Assignment 4 Solve the differential equation. It is important that you show all of your steps...
Chapter 9, Section 9.4, Question 013 The rate at which a drug leaves the bloodstream and passes into the urine is proportional to the quantity of the drug in the blood at that time. If an initial dose of Qo is injected directly into the blood, 27% is left in the blood after 4 hours. (a) Write and solve a differential equation for the quantity, Q. of the drug in the blood after t hours. Use k as the positive...
show works please 10 Points The differential equation shown below models the temperature of an 89° C cup of coffee in a 17° C room, where is it known that coffee cools at a rate of 1° C per minute. Solve the differential equation to find an expression for the temperature of the coffee at time t. 0 In the differential equation shown below y is the temperature of the coffee in C, and t is the time in minutes...
show works please 10 Points The differential equation shown below models the temperature of an 89° C cup of coffee in a 17° C room, where is it known that coffee cools at a rate of 1° C per minute. Solve the differential equation to find an expression for the temperature of the coffee at time t. 0 In the differential equation shown below y is the temperature of the coffee in C, and t is the time in minutes...
Solve differential equation with initial condition. Final answer in form y=f(x). Please show all steps, thank you!!! dy = xy² + 4x y dx yo) = 2
Q.1 Solve the following differential equation in MATLAB using solver ‘ode45’ dy/dt = 2t Solve this equation for the time interval [0 10] with a step size of 0.2 and the initial condition is 0.
Please show all the steps of these questions. Solve the differential equation y' + y cos x = { sin 2x dy V1 - y2 Solve the initial value problem y(e) = dx x In (x) 1 = V2
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...
Show all steps please. b. ASSUME the Differential Equation: dx dt :-(W2)x. 1. SOLVE. That is, determine a function x = f(t) which satisfies the above. 2. CHECK. Show that your function to the above dif. eg. is, indeed, a solution.
problem 1) Find the differential equation describing the amount of salt,Qb, in the tank for times t in the interval t>=T. Then solve to obtain Qb(t) for t>= T A Water Tank Problem with Discontinuous Source A water tank contains V > 0 liters of pure water and Qo grams of salt. At time t = 0 we start pouring water into the tank with a rate r >0 liters per minute with a salt concentration of q> 0 grams...
please show all steps 4. Some equations that are not separable can be made separable by an appropriate substitution. Differential equations of the form y = f (!) are called Euler-homogeneous. These can be solved by letting v = y/t or y = ut. Using the product rule, dy du di = v + tai so that the differential equation becomes du v+t du f(0) - 0 dt t Use this technique to solve dy 2y+ + +4 - Leave...