MA232 Mid_Term Review I

MA232 Mid_Term Review I - 1. Solve the following dierential...

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1. Solve the following di/erential equations using elementary methods you like. For each problem, &nd a general solution. If the problem has boundary conditons, &nd a particular solution responding to the given boudary conditions. 1) y 0 = 1 + x + y + xy 2) x dy dx & y = 2 x 2 y; y (1) = 1 3) xy 0 = 2 y + x 3 cos x; y ( & ) = 2 4) 2 xy 0 + y = 10 p x 5) xy 2 dx dy = x 3 + y 3 ; y (1) = 0 2 : Find the roots of the equation 1) z 3 + 1 = 0 2) z 2 + 3 z + 3 = 0 3 A = & 2 1 4 3 ± ; B = & & 1 0 4 3 & 2 5 ± ; Find AB; and BA 4 C = & 1 & 1 1 1 ± ; Find C & 1 , and det C 5 : An arrow is shot straight upward from the ground with an initial velocity of 160 ft±s. It experiences both the deceleration of gravity and deceleration v 2 = 800 due to air resistance. How high in the air does it go? 6. During the period from 1790 to 1930 , the U.S. population P ( t ) ( t in years) grew from 3.9 million to 123.2 million. Throughout this period , P ( t ) remained close to the solution of the initial value problem dp dt = 0 : 03135 P & 0 : 0001489 P 2 ; P (0) = 3 : 9 (a) What 1930 population does this logistic equation predict?
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MA232 Mid_Term Review I - 1. Solve the following dierential...

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