Question
Solve: .
Answer :
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We are asked to solve the differential equation numerically: [ \frac{dy}{dx} = \frac{1}{x + y + 1}. ] Let us solve it using Euler’s Method. We assume an initial value; for numerical solutions, we typically need (y(x_0) = y_0). Since it is not given, let's assume (x_0 = 0, y_0 = 0) and choose a step size (h = 0.1). Euler’s formula is: [ y_{n+1} = y_n + h f(x_n, y_n), \quad f(x, y) = \frac{1}{x + y + 1}. ] Step 0: (x_0 = 0, y_0 = 0) [ y_1 = y_0 + h f(x_0, y_0) = 0 + 0.1 \cdot \frac{1}{0 + 0
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