ENGR 213 Study Guide - Final Guide: Scilab, Diagonalizable Matrix

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Solve the following rst order odes by nding the general solution and the solution of the ivp (when given). (a) (cid:18) 2x x2 + y2 + x2 (b) px6 + 1 y = (c) y = 2 + ey 2x+3. 6x5 y2 , y(0) = 2 x2 + y2. [hint: substitution of the form u = ax + by + c] Solve the following linear odes by nding the general solution and the solution of the ivp (when given). (a) (b) d4y dx. Xy + y = x2 ln(x) , (x > 0), (cid:26) y(1) = 0 y (1) = 2. [20 pts] problem 3 (a) find the center, the radius of convergence and the interval of convergence of the following power series. 3n(x 2)n n2 (b) find the general solution as a power series centered at the regular point x = 0 and up to degree 4 of the di erential equation below. y + (x 1)y = 0.