make a first order differential equation from a problem in real life and give an explanation...

make a first order differential equation from a problem in real life and give an explanation and derivative (the proof) of the formula

Expert Solution

We are modelling exponential growth with a first order differential equation.

Taking into account a real life problem: A population of a small town grows proportionally to its current population with the assumption that initial population is 5000( say) and grows at the rate of 4% per year.

Tha problem has been solved in the solution provided below.

Colby Messinger answered 6 months ago

Discuss a real time application of first order differential equation [Answer should include literature review and...

Discuss a real time application of first order differential equation [Answer should include literature review and real applications maximum 200 words].

1. Give an example of a 3rd order nonlinear ordinary differential equation.

How do we find singular solutions for a first order Differential Equation?

Find the particular solution of the first-order linear differential equation for x > 0 that satisfies...

Find the particular solution of the first-order linear differential equation for x > 0 that satisfies the initial condition. (Remember to use absolute values where appropriate.) Differential Equation Initial Condition x dy = (x + y + 7) dx y(1) = 6 y =

Writing Prompt(s) One method for solving a system of first order linear differential equation such as...

Writing Prompt(s) One method for solving a system of first order linear differential equation such as x ′ = a x + b y y ′ = c x + d y is to take the derivative of the first equation and use the second equation to ``decouple'' the system and create a second order equation, which we can solve using our previous techniques. Does this always work? If not, what conditions on the constants a, b, c, and d...

This is a Matlab Question Create MATLAB PROGRAM that can solve First Order Linear Differential Equation...

This is a Matlab Question Create MATLAB PROGRAM that can solve First Order Linear Differential Equation ( 1 example contains condition and the other does not have condition). 1. ty′ + 2y = t^2 − t + 1, y(1)=12 The correct answer is y(t) = 1/4 t^2 − 1/3 t + 1/2 + 1/12t^2 2. (x-1) dy/dx + 2y = (x+1)^2 The correct answer is y = (x(x+1) / x-1 ) + C(x+1) / x-1 The correct answer is

I need a step by step explanation to the following problem in order to make me...

I need a step by step explanation to the following problem in order to make me understand the solution: 14-23 Flexible Budgets and Operating-Income Variance Analysis: Spreadsheet Application The following information is available for Brownstone Products Company for the month of July: Actual Master Budget Units 3,800 4,000 Sales Revenue 53,200 60,000 Variable manufacturing costs 19,000 16,000 Fixed manufacturing costs 16,000 15,000 Variable selling and administrative expenses 7,700 8,000 Fixed selling...

Determine the solution of a homogeneous linear first order Ordinary Differential Equation system: (use 2 methods,...

Determine the solution of a homogeneous linear first order Ordinary Differential Equation system: (use 2 methods, substitution method, and matrix method) x1' = - 4x1-6x2 x2' = x1+ x2 With the initial values: x1 (0) = 2 ; x2 (0) = -1 b. x1' = -x2 x2' = -x1 With initial values: x1 (0) = 3 ; x2 (0) = 1

Solve the following problems. a) What is the order of the differential equation ? ′ =...

Solve the following problems. a) What is the order of the differential equation ? ′ = ? 2 − 3? − 10? Is it linear ? b) Determine whether the differential equation ? ′ = ? 2 − 3? − 10 possesses constant solutions. If yes find these constant solutions. c) Find the value(s) of ? so that the function ? = ? ?? is a solution of ? ′′ − 3? ′ − 10? = 0. Do you think...

Solve the initial value problem (first state the type of the differential equation) y'(x) = (2xy)...

Solve the initial value problem (first state the type of the differential equation) y'(x) = (2xy) / (x^2−y^2) & y(1) = 1

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