MATH 246 Final: MATH246 ALL-SECTIONS FALL2012 0000 FINAL EXAM
15 Feb 2019
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Answer only one question on each answer page. Write your name and which question is being answered on each answer page. Sign the honor pledge on the first answer page only. Indicate your answer to each part of each question clearly. Give reasoning that justifies your answers. (1) [28] give the explicit solution to each of the following initial-value problems. Identify their intervals of definition. (a) v" = t. 12 ~, v(5) = -3. vyt2 -16 ey -2x (b) y"+=o, xey y(1)=2. (2) [15] let y(t) be the solution of the initial-value problem y" = 2t -y2 , y(o) = 1 . Approximate y(0. 2) with one step of the improved ~uler (runge-trapezoidal) method. (3) [28] give the explicit solution to each of the following initial-value problems. Ypu should try to evaluate any definite integrals that arise. (5) [15] consider the following matlab commands and the resulting output. syms t s y; eqn = sym("d(d(y))(t) = heaviside(t -1)
