3. Given the ordinary differential equation: (x-2y) dx And the initial condition y(0) = 1, approximatey(0.5)...
Find the solution of the differential equation with the given initial condition. Dy/dx = 2x + sec^2x/2y, y(0) = 5.
7. Given the differential equation y' = 4x – 2y; y(1) = 0.5, use Euler's method, with a step size (Ax or h) of 0.25 to approximate y(2). Show appropriate steps.
QUESTION 9 Consider given ordinary differential equation, y"+y" - 2y = 0, y(t = 0) = 0, y'(t = 0) = 1. What is the y at t= 0.2 when the equation is solved using finite difference method with At = 0.12 Use central difference approximation for y" and y'. Note: to receive the credit, the final numeric answer MUST be within the range of plus/minus 0.02. Use the 4 significant digits for the step-by-step calculation and final answer, i.e.,...
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equation numerically over the interval 0 s i s 2.0 and a step size h At 0.5.A Apply the following Runge-Kutta methods for each of the step. (show your calculations) i. [0.0 0.5: Euler method ii. [0.5 1.0]: Heun method. ii. [1.0 1.5): Midpoint method. iv. [1.5 2.0): 4h RK method...
1. Solve the following initial value problem over the interval from x- 0 to 0.5 with a step size h-0.5 where y(0)-1 dy dx Using Heun method with 2 corrector steps. Calculate g for the corrector steps. Using midpoint method a. b. 1. Solve the following initial value problem over the interval from x- 0 to 0.5 with a step size h-0.5 where y(0)-1 dy dx Using Heun method with 2 corrector steps. Calculate g for the corrector steps. Using...
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...
For the following differential equation: (x^3)dy/dx+y^4+3=0 where dy/dx is the first derivative of y with respect to x, () means power. The equation has initial values y=2.00 at x=1.00 Using Euler method with a step in the x direction of h=0.30: Show the equation to use to generate values of (2 marks) Calculate the missing values of y in the table below I .1.30 1.00 2.00 1.60 For (2 marks)
8. Solve the following differential equation given the initial condition y(0) = -5: dy 2.c dr 1+22 9. Solve the following differential equation using the method of separation of variables: dy = x²y. dic
Find a function y=f(x) satisfying the given differential equation and the prescribed initial condition. 1 dy dx y(7) = -5 1x + 2
Solve the differential equation with the given initial condition. y' + 2xy = 8x y(0) = 0 y(x) =