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Unformatted text preview: Math 16B Spring 2011 Sarason REVIEW EXERCISES 2 1. Perform the integrations. (a) Z tan x cos 3 x dx (b) Z tan x cos 3 x dx (c) Z 1 x ( x 1) 4 dx (d) Z 1 x 2 ( x 1) 5 dx (e) Z 4 e x dx (f) Z 1 x  5 dx (g) Z 1 x 1 . 0001 dx (h) Z 1 x e dx 2. Find the general solution of the differential equation y = 3 y 2 t and the solutions satisfying the initial conditions y (1) = 1 and y (1) = 0. 3. Find the general solution of the differential equation 2 yy = ( y 2 1) 2 and the solutions satisfying the initial conditions y (1) = 2 and y (1) = 1. 4. Find the general solution of the differential equation y = ( t 1) 2 ( y + 1) 4 and the solutions satisfying the initial conditions y (0) = 1, y (0) = 0, y (0) = 1. 5. Find the general solution of the differential equation y = y 5 t . 6. Find the solutions that are defined for all t of the differential equation y = e y cos t . 7. Find the general solution of the differential equation y = t (1 + y ) in two ways: by separation of variables, and by the method for solving linear firstorder ODEs.of variables, and by the method for solving linear firstorder ODEs....
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This note was uploaded on 04/16/2011 for the course MATH 16B taught by Professor Sarason during the Spring '06 term at University of California, Berkeley.
 Spring '06
 Sarason
 Math, Calculus

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