MATH-0042 Final: w12finalsol
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Solutions to math 42 final exam march 19, 2012: (12 points) consider the initial value problem (a) use euler"s method with step size 0. 1 to nd an approximation to y(0. 3). = ln y dy dx y(0) = 2 you do not need to simplify your answer. (4 points) we begin with the initial values x0 = 0, y0 = 2 and compute three steps: n xn. [2 0. 1(ln 2)] 0. 1 ln[2 0. 1(ln 2)] Thus, euler"s method nds that y(0. 3) is approximately. Substituting this into the di erential equation, we nd 0 = ln c, so c = 1. Thus, the only equilibrium solution is the function y(x) = 1. Brie y explain your reasoning. (3 points) as x , we have that y(x) approaches 1; the function y(x) is decreasing and concave up whenever y > 1, and y will approach the equilibrium solution. d2y.
