exam1sampleq - Sample questions for Exam 1 1. Verify that 1...

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Sample questions for Exam 1 1. Verify that 1 x + 1 is a solution to the equation (1 + x ) y 00 + (1 - x ) y 0 - y = 0. 2. Find the general solution to dy dx = xe x + y . 3. Solve the initial value problem dy dt = y 2 - y 2 cos x , y (0) = 3. 4. Find the general solution to dy dt = y t + 1. 5. Find the solution to the initial value problem dy dx = - 2 y + xe - x , y (0) = 2. 6. Find the general solution to y 00 - 4 y 0 - 5 y = 0. 7. Find the general solution to y 000 + 2 y 00 - 8 y 0 = 0. 8. Solve the initial value problem y 00 - 6 y 0 + 8 y = 0 , y (0) = 3 , y 0 (0) = - 2 . 9. Perform two steps of Euler’s method with step size 1 4 to approximate the solution of dy dt = t - y + 2 , y (0) = 3 at t = 1 2 . 10. Let y ( x ) be the solution of the initial value problem dy dx = 1 + y 2 3 , y (1) = 1 . Use two steps of Euler’s method with h = 1 2 . Note for problems 9 and 10: The formula for Euler’s method is y n +1 = y n + f ( t n , y n ) h . (This formula will be provided on the exam.) 11. Find the Wronskian of
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This note was uploaded on 04/23/2008 for the course PH 132 taught by Professor Ramsdell/wick during the Fall '08 term at Clarkson University .

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exam1sampleq - Sample questions for Exam 1 1. Verify that 1...

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