Tutorial 1 (week january 11)

Tutorial 1 (week january 11) - 1 Solve the initial value...

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MATH 1005BC Tutorial Questions Week of January 11, 2010 1 Instructor: Dr. A. Alaca Multiple Choice Questions. 1. If y = 2 xy and y (0) = 1, then what is y ? (a) e 2 x (b) e x 2 (c) e 1 2 x 2 (d) e x 2 2. If y + y = 1 and y (0) = 2, then what is y ( - 2)? (a) e 1 (b) e (c) e 2 (d) 1 + e 2 3. If y is the solution of the initial value problem y + 1 x y = 10 x 3 , y (1) = 1 , what is y ( - 1) ? (a) - 1 (b) 2 (c) - 2 (d) 3 4. If y + 1 x y = x 3 and y (1) = 2 5 , then what is y ? (a) 1 5 ( x 4 + x 1 ) (b) 1 5 ( x 2 + x 2 ) (c) 1 5 ( x 3 + x ) (d) 1 5 ( x 4 + x 2 ) 5. If y is the solution of the initial value problem y = e x 2 y y (0) = 3, what is y (1) ? (a) e + 1 (b) e + 1 (c) e + 8 (d) e + 8 (e) - e - 8 6. What is the diFerential equation satis±ed by the orthogonal trajectories to the curves y = kx 5 . (a) y = 5 y x (b) y = - x 5 y (c) y = 5 y x (d) y = - x 5 y
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MATH 1005BC Tutorial Questions Week of January 11, 2010 2 Long Answer Questions. Show all your work.
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Unformatted text preview: 1. Solve the initial value problem y ′ = (2 x-3 x 2 ) y , y (0) =-2. 2. Solve the diferential equation 2 x cos y-x 2 sin y y ′ = 0 , y (1) = 1 . 3. Solve the diferential equation (3 y 3 + 5 x 2 ) dx + (3 xy 2 ) dy = 0. 4. Solve the diferential equation y ′ + 1 x y = cos x . 5. Solve the diferential equation y ′-2 x y = x 3 e x . 6. Find the general solution o± the diferential equation y ′-y cos x = 2 xe sin x . 7. Solve the diferential equation y ′ + 2 xy = x y 5 . 8. Find the general solution o± the diferential equation y ′ + y = 2 xy 2...
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Tutorial 1 (week january 11) - 1 Solve the initial value...

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