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.

Step-by-step explanation:

Given is a differential equation

Here we have

To find y1, y2, y3, y4

Step size = 0.5

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

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step-by-step explanation: