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Unformatted text preview: y = 2 + (2 ty ) 3 on 0 ≤ t ≤ 3 ,  y  ≤ 4 P = (2 , 1) b) y + 2 y = et on  t  ≤ 2 ,  y  ≤ 3 P = (0 , 0) c) y = tsiny on 0 ≤ t ≤ 10 , ≤ y ≤ 10 P = (2 , 2) Problem 4. Classify each equation as linear or nonlinear. a) y + e t y = 4 b) e t y = t2 y c) y y 000 + 4 y = 3 t d) y 00 = t 3 y e) y y = t + y f) ye y = sint Problem 5. (Bernoulli equation.) y + p ( t ) y = q ( t ) y n , where n is a constant 1 2 is called Bernoulli’s equation. a) Give the general solution of the Bernoulli’s equation for n = 0 and n = 1. b) If n is neither 0 nor 1, then the Bernoulli’s equation is nonlinear. Nevertheless, show that by transforming the dependent variable y ( t ) to v ( t ) = y 1n , ( n 6 = 0 , 1) , the Bernoulli’s equation can be converted to the equation: v + (1n ) p ( t ) v = (1n ) q ( t ) which is linear. Find the general solution to the Bernoulli’s equation....
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This note was uploaded on 05/25/2008 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Fonken
 Math, Calculus

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