Q14Advanced Engineering Mathematics

Question

Using Euler method find the value of y (0.025) . Given \frac{d y}{d x} = x + y + x y; y (0) = 1 and h = 0.025.

Answer 1

Euler's method is a first-order numerical procedure for solving ODEs with a given initial value. We are given the derivative function $f (x, y) = x + y + x y$ , the initial condition $x_{0} = 0$ , $y_{0} = 1$ , and the step size $h = 0.025$ .

Using Euler's iteration formula: $y_{1} = y_{0} + h f (x_{0}, y_{0})$ . Substituting the given values, we get: $y_{1} = 1 + 0.025 (0 + 1 + (0) (1)) = 1 + 0.025 (1) = 1.025$ . Therefore, the approximate value is $y (0.025) = 1.025$ .

Q14Advanced Engineering Mathematics

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