midrev1 - (2 xy 3 + 3 x 2 + 2 y ) dx + (3 x 2 y 2 + 2 x )...

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MAP 2302 Fall 2010 Review for Midterm 1. Format: 5 problems, 20 points each, closed books/notes, scientific calculators only. NO GRAPHIC CALCULATORS. Time allowed: 50 minutes. Equation Types: separable, linear, exact equations, special integrating factors, substitutions (only those covered in class), solving initial-value problems. Practice Problems: (1) Find the general solution of dy dx = 1 + x x - xy 2 . (2) Solve the initial value problem dx dt = 3( x - 1) t, x (0) = 0 . (3) Find the general solution of du dt + u = e - t . (4) Solve the initial-value problem dy dx = y + 1 , y (0) = 0 . (5) Solve the initial value problem ( y 2 + e x ) · dx + (2 xy ) · dy = 0 , y (1) = 0 . (6) Find the general solution of
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Unformatted text preview: (2 xy 3 + 3 x 2 + 2 y ) dx + (3 x 2 y 2 + 2 x ) dy = 0 . (7) Find an integrating factor = ( x ) or = ( y ), and solve the equation (2 xy ) dx + ( y 2-3 x 2 ) dy = 0 . (8) Solve y dx dy + x = y 2 . (9) Find the general solution of dr d = e r-3 . (10) Solve the initial value problem dy dx = x 2 + xy + y 2 x 2 , y (1) = 0 . Additional problems: 1-39 (odd) on pages 81-82; plus the homework problems. The key will be posted as a separate le. We will spend the class on 09/15/10 discussing (some of) the above problems....
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