Using h = 0.1, approximate the value of y(0.5) for the given differential equation using a) Improved Euler method, and b) 4th order Runge-Kutta method. Show your solutions for the first, third, and last row. No rounding off computed values. y′ = y + 2x − x2 y(0) = 1

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Chapter2: Second-order Linear Odes
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Using h = 0.1, approximate the value of y(0.5) for the given differential equation using a) Improved Euler method, and b) 4th order Runge-Kutta method. Show your solutions for the first, third, and last row. No rounding off computed values.

y′ = y + 2x − x2

y(0) = 1

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