Question

Use Euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3 and y4 of the solution of the initial-value problem y' = y − 3x, y(4) = 2.

Answer 1

Answer:

Step-by-step explanation:

Given is a differential equation

$y' = y − 3x, y(4) = 2$

Here we have $x_0 = 4 and y_0 =2$

To find y1, y2, y3, y4

Step size = 0.5

$x_1=4.5, x_2 =5,...$

y_1 = y_0 +0.5f(x_0,y_0)

Here f(x,y) = y-3x

Applying this successively we get

y1 = 2+0.5(2-12) = -3

y2 = -3+0.5(-3-13.5) = -11.25

y3 =-11.25+0.5(-11.25-15) =-24.375

y4=-24.375+0.5(-24.375-16.5)=-44.8125