23F07-Exam1Practice-1

23F07-Exam1Practice-1 - t " y + ( t + 1) y = t...

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Math 3323 - Fall 2007 Exam 1 Practice Problems 1. For the differential equation " y = y ( y # 2) 2 , (a) Find the equilibrium solutions. (b) Determine whether each is stable or unstable. (c) Determine the behavior of the solution y as t "# . If this behavior depends on the initial value of y at t = 0 , describe this dependency. (Note: This problem should be done without solving the d.e.) 2. (a) Use Euler’s method with a step size of h = 0.2 to approximate the solution of the initial value problem dy dt + 1 2 y = 3 2 " t , y (0) = 1 on the interval 0 " t " 1 . (b) The IVP in part (a) is first order linear—Solve it analytically. 3. Solve the first order linear initial value problem
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Unformatted text preview: t " y + ( t + 1) y = t , y (ln2) = 1, t > . 4. Solve the separable initial value problem " y = (1 # 2 x ) y 2 , y (0) = # 1/6 . 5. Solve the exact initial value problem (2 x + y 2 ) dx + 2 xydy = 0, y (1) = 10 6. Find the general solutions of the following differential equations of varying type. (Leave the solutions in implicit form if they come out that way.) (a) ( e x sin y " 2 y sin x ) dx + ( e x cos y + 2cos x ) dy = (b) " y + 2 ty = 2 te # t 2 (c) dy dx = x " e " x y + e y 7. Determine the values of m for which y = e mx is a solution to the 2 nd order linear differential equation 2 " " y # 3 " y + 2 y = ....
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