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For the following differential equation: (x^3)dy/dx+y^4+3=0 where dy/dx is the first derivative of y with respect...
3. Consider the differential equation dy 2x2y dx 0, y 1 In the following questions work to 4 decimal places with the initial conditions x = throughout and give your answer to 3 decimal places, or use exact fractions (a) Use the Euler method to calculate an estimate of the value of y after four steps of length h 0.5 [4 marks] (b) Use the Modified Euler method to calculate an estimate of the value of y after two steps...
The differential equation : dy/dx = 2x -3y , has the initial conditions that y = 2 , at x = 0 Obtain a numerical solution for the differential equation, correct to 6 decimal place , using , The Euler-Cauchy method The Runge-Kutta method in the range x = 0 (0.2) 1.0
a) Consider the first-order differential equation (y + cos.r) dx + dy = 0. By multiplying integrating factor y(x) = ei" to both sides, show that the differential equation is exact. Hence, solve the differential equation. (6 marks) b) Solve the differential equation (4.r + 5)2 + ytan z = dc COSC (7 marks)
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y (a) Show that 01 (C) = e is a solution. (b) Show that 02 (2) = e-* is a solution. (c) Show that 03 (x) = xe-" is a solution. (d) Determine the general solution to this homogeneous differential equation. (e) Show that p (2) = xe" is a particular solution to the differential equation dy dy dy dx3 d.x2 - y = 4e*...
Consider the differential equation dy/dx = (y-1)/x. (a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated. (b) Let y = f (x) be the particular solution to the given differential equation with the initial condition f (3) = 2. Write an equation for the line tangent to the graph of y= f (x) at x = 3. Use the equation to approximate the value of f (3.3). (c) Find the particular solution y...
Solve the differential equation: (3- x?) y dy dx y +3/7–3
Help with these questions please. A mathematical model has been described by an engineer into the following differential equation: dy dx y(0) 2.5 Demonstrate an Euler method simulation of y versus x with a tabular algorithm using Ax 0.5 and 0.0 X 3.0. Demonstrate a 4th-order Runge Kutta method simulation of y versus x with a tabular algorithm using What can you say about y(x) and the methods used? a. b. Ax 0.5 and 0.0 3.0 x c. A mathematical...
Find the solution of the differential equation dy dx = x y that satisfies the initial condition y(0)=−7. Answer: y(x)=
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
First, verify that y(x) satisfies the given differential equation. Then, determine a value of the constant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator to sketch several typical solutions of the given differential equation, and highlight the one that satisfies the given initial condition. y' =y+3; y(x) = CeX-3; y(0) = 8 What step should you take to verify that the function is a solution to the given differential equation? O A. Differentiate...