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Unformatted text preview: . a) y = 2 xy y (0) = 0 , y (0) = 2 , y (0) = 1 , y (1) =5 b) y y + x = 0 y (0) = 4 , y (3) = 0 , y (3) = 0 , y (3) =4 c) y = tany y (3) = 2 , y (3) = 0 , y (0) = 2 . Problem 3. Show that equation is exact and obtain its general solution.Also, ﬁnd the particular solution corresponding to the given initial condition. a) ( sin ( xy ) + xy cos ( xy )) dx + x 2 cos ( xy ) dy = 0 , y (2) =1 b) 3 x 2 sin (2 y )2 xy ) dx + (2 x 3 cos (2 y )x 2 ) dy = 0 , y (1 / 2) = 3 . 1 c) 3 x 2 y ln ( y ) dx + ( x 3 ln ( y ) + x 32 y ) dy = 0 , y (8) = 3 d) 3 dxdy = 0 , y (0) = 6 1 2 Problem 4. (Euler’s Method.) Use the Euler method to compute, by hand, y 1 , y 2 and y 3 for the speciﬁed initial value problem using h = 0 . 2. a) y =y, y (0) = 1 b) y = 1 + 2 xy 2 , y (1) =2 c) y = x 2y 2 , y (3) = 5 d) y = tan ( x + y ) , y (1) = 2 e) y = √ x + y, y (0) = 3 Problem 5. Solve problems 1 to 7 from Chapter 2, Section 5 of the course textbook....
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 Spring '08
 Fonken
 Math, Calculus

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