2. (25%) Consider the following first order differential equation. dx = (t t 1) y(0) =...

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2. (25%) Consider the following first order differential equation. dx = (t t 1) y(0) = 1 (a) Find the value of the y at t=2 using the midpoint method and step size of h=1. (b) Formulate (but do not solve!) a Runga-Kutta method that uses the slope at the beginning, middle and end of an interval. The method gives the first slope twice as much weight as the middle slope which has twice as much weight at the last slope. 2. (25%) Consider the following first order differential equation. dx = (t t 1) y(0) = 1 (a) Find the value of the y at t=2 using the midpoint method and step size of h=1. (b) Formulate (but do not solve!) a Runga-Kutta method that uses the slope at the beginning, middle and end of an interval. The method gives the first slope twice as much weight as the middle slope which has twice as much weight at the last slope.