MATH 307 Midterm: MATH 307 UW 307C Sp06 Sol2
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Math 307, section c, spring 2006, solutions to midterm ii: find the general solution of the di erential equation. 2x2y + xy 6y = 0 given that y = x2 is a solution. Then y = v x2 + 2xv and y = v x2 + 4xv + 2v. Substituting these into the di erential equation and collecting terms. 2x4v + (8x3 + x3)v + (4x2 + 2x2 6x2)v = 0. Then we have the rst order linear di erential equation whose solution is given by. 2x dx = x 9/2. v = z x 9/2dx = 2. The general solution of the di erential equation is y(t) = c1x2 + c2x 3/2. 1: a spring is streched 3 in. by a 3-lb weight. The 3-lb weight is started from the equilibrium point with a downward velocity of 6 ft/sec. The air resistance furnishes a retarding force of magnitude 0. 01 of the velocity.
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