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### prob2-4

Course: MAP 3202, Fall 2011
School: Valencia
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Word Count: 145

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2-4 Problem 1. Test the following for exactness and solve: 2 2 a. x y dy y x dx 0 b. e cos ydx e sin ydy x x c. ax by dx bx ay dy 0 2 d. 4 y 2 2 x2 8 y 2 x2 dx 3 2 dy 0 4 xy 2 x3 4y x y 2. Solve: DE: 2 x 1 y 3 dx 3 x 1 y 2 2 y dy 0 IC: y 1 3 3. Derive the following solution of the initial-value problem (40): x x0 M x, y0 dx N x, y dy 0 y y0 4. Explain why a...

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2-4 Problem 1. Test the following for exactness and solve: 2 2 a. x y dy y x dx 0 b. e cos ydx e sin ydy x x c. ax by dx bx ay dy 0 2 d. 4 y 2 2 x2 8 y 2 x2 dx 3 2 dy 0 4 xy 2 x3 4y x y 2. Solve: DE: 2 x 1 y 3 dx 3 x 1 y 2 2 y dy 0 IC: y 1 3 3. Derive the following solution of the initial-value problem (40): x x0 M x, y0 dx N x, y dy 0 y y0 4. Explain why a differential that equation is not exact cannot be solved by integrating both sides as in Eqs. (41) and (42). 5. Assume the equation y 2 sin xdx yf x dy 0 is exact. Find all possibilities for f x . Answer 2-4 1. a. xy c. 2. 1 3 1 3 x y c b. e x cos y c 3 3 1 a x 2 y 2 bxy c d. ln xy 4 y 2 x 2 c 2 2 x 1 y3 y 2 9 5. f x c 2 cos x
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Valencia - MAP - 3202
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Valencia - MAP - 3202
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Supplementary problems for chapter 2 1. 2. 3. 4. 5. 6. 7. 4 x 6 xy dx 6 x y 3 y dy 0 1 u d 1 du 1 x y dx x y x dy 03 2 2 2 2 2 2 2 3dy y tan x 2 x dx2 x3 dy 1 3x 2 y dx 0y 1 e x e yx 2 y xy 2 y 2 0 dN 8. DE: kN c N dt dN IC: kN c N dt dx 9. DE: a x
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