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Differential equations: slope fields and Euler's method
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Learn it A differential equation like dy/dx = x + y gives the slope at every point; a slope field draws those slopes. Euler's method steps along: yₙ₊₁ = yₙ + h·(slope at (xₙ, yₙ)).
Example: dy/dx = x + y, y(0) = 1, step h = 0.5. Estimate y(0.5).
- Slope at (0, 1) = 1.
- y(0.5) ≈ 1 + 0.5(1) = 1.5.
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