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Unformatted text preview: x ≥ 0: y = x − 1 + 2 e − x , ≤ x ≤ 2; x 3 − 1 9 + ³ 4 9 e 6 + 2 e 4 ´ e − 3 x , 2 < x. (e) The graph of the solution is given in ±igure B.18 of the answers in the text. 33. (a) Writing the equation in standard form yields dy dx + 2 x y = 3 . Therefore, P ( x ) = 2 /x and µ ( x ) = exp ³Z 2 x dx ´ = exp (2 ln  x  ) =  x  2 = x 2 . Hence d dx ( x 2 y ) = 3 x 2 ⇒ x 2 y = Z 3 x 2 dx = x 3 + C ⇒ y = x + C x 2 53...
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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