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# practice1 - people who have not yet heard it How long will...

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Practice Exam 1a 1. Solve the IVP: (1 + e x ) dy dx = y , y (0) = 2. 2. Solve the ODE: dy dx = 1 + x 1 + y . 3. Solve the ODE: 2( e y + x 3 e 2 x ) dx - xe y dy = 0. 4. 100L of a brine solution is diluted with pure water at a rate of 2L/min and drained at a rate of 1L/min. If the tank begins with 100g of salt, how long until it contains only 50g? Practice Exam 1b 1. Solve the IVP: dy dx = 4 x 3 y - y , y (1) = - 3. 2. Solve the ODE: (3 y + x 4 cos x ) dx - xdy = 0. 3. Solve the ODE: (1 + t 2 ) y 0 + 4 ty = 1 1 + 2 t + t 2 . 4. A rumour begins to spread in a town of 100,000. Within a week, 10,000 people have heard the rumour. Assume the rate it spreads is proportional to the number of
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Unformatted text preview: people who have not yet heard it. How long will it be until half the city has heard the rumour? Practice Exam 1c 1. Solve the ODE: xy 00 = y . 2. Solve the IVP: (1 + x 2 ) dy dx = y , y (0) = 2. 3. Solve the ODE: dy dx =-cos x + ln y x y + e-y . 4. Sketch a slope ﬁeld and use Euler’s method (with step ε = 1) to approximate y (2): y = x + 1 2 y 2 , y (-2) = 0. y (2) = 1...
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