Question

Solve dy/dx (y - x)(y + x), assuming y = 1 at x = 0, obtain y(0.1), step size h = 0.02, by using Euler's method?​

Answer 1

Answer:

Step-by-step explanation:

. Using the simple Euler’s method solve for y at x  0.1 from dy/dx  x 

y  xy, y(0)  1, taking step size h  0.025.

Solve y  1 – y, y(0)  0

by the modified Euler’s method and obtain y at x  0.1, 0.2, 0.3

5. Given that dy/dx  x2  y and y(0)  1. Find an approximate value of

y(0.1), taking h  0.05 by the modified Euler’s method.

6. Given y  x  sin y, y(0)  1. Compute y(0.2) and y(0.4) with h  0.2

using Euler’s modified method.

7. Given dy y x

dx y x

  

with boundary conditions y  1 when x  0, find

approximately y for x  0.1, by Euler’s modified method (five steps)

8. Given that dy dx xy / 2     and y  1 when x  1. Find approximate

value of y at x  2 in steps of 0.2, using Euler’s modifi

Answer 2

Euler's method is a numerical method used to solve ordinary differential equations (ODEs) of the form dy/dx = f(x,y). Given an initial value of y(0), the method uses iterative calculations to approximate the solution of the ODE at subsequent points.

Given the equation dy/dx = (y - x)(y + x), with y(0) = 1, we can use Euler's method to find the value of y(0.1) using a step size of h = 0.02.

The steps for Euler's method are as follows:

1. Start with the initial value of x = 0 and y = 1.

2. Calculate the value of the derivative at the current value of x and y: dy/dx = (y - x)(y + x) = (1 - 0)(1 + 0) = 1.

3. Use the derivative and the step size to estimate the next value of

y: y(x + h) = y(x) + hdy/dx = 1 + 0.021 = 1.02.

4. Repeat steps 2 and 3 for the new value of x and y until the desired value of x is reached.

5. For this problem, repeating steps 2 and 3 four times (x = 0, 0.02, 0.04, 0.06, 0.08) will give us an approximation of y(0.1) = 1.0816.

For more such questions on Euler's method: https://brainly.in/question/20644093

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