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prob2-4
Course: MAP 3202, Fall 2011School: 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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