Question

Euler’s method find approximate value of y at x = 1 in five step taking h=0.2 given = + 0 = 1.

Answer 1

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Consider below differential equation

dy/dx = (x + y + xy)

with initial condition y(0) = 1

and step size h = 0.025.

Find y(0.1).

Solution:

f(x, y) = (x + y + xy)

x0 = 0, y0 = 1, h = 0.025

Now we can calculate y1 using Euler formula

y1 = y0 + h * f(x0, y0)

y1 = 1 + 0.025 *(0 + 1 + 0 * 1)

y1 = 1.025

y(0.025) = 1.025.

Similarly we can calculate y(0.050), y(0.075), ....y(0.1).

y(0.1) = 1.11167