Midterm1+with+solutions

Midterm1+with+solutions - Consider the following system of...

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MAE 140 Midterm Examination #1 Tuesday, October 30, 2007, 9:30am – 10:50am, SSPA 1100 Total Possible Score: 20 Points. No Books/Notes/Calculators/Computers/Phones. Problem 1 (10 Points): Single Ordinary Differential Equation Consider this single ordinary differential equation (ODE) for y x with x 0 : ln x 2 dy dx y x 6x = 0 where ln x denotes the natural logarithm of x . (3 Points) Show that the ODE is exact. (4 Points) Find the general solution for y x by using the method for exact ODE's or any other analytical method of your choice. (3 Points) Find the particular solution for y x that satisfies the condition y 1 = 2 . Problem 2 (10 Points): System of Ordinary Differential Equations
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Unformatted text preview: Consider the following system of ordinary differential equations (ODE's) for x 1 t and x 2 t which can be shown to arise from the flow and mixing of water with salt between two interconnected tanks: d dt x 1 x 2 = − 1 10 3 40 1 10 − 1 5 x 1 x 2 with initial condition x 1 x 2 = − 17 − 21 . (10 Points) Find the particular solutions for x 1 t and x 2 t that satisfy the above system of ODE's and the initial condition, by using the matrix method based on eigenvalues/eigenvectors or any other analytical method of your choice....
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This note was uploaded on 08/31/2010 for the course ENGRMAE 140 taught by Professor Staff during the Fall '08 term at UC Irvine.

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Midterm1+with+solutions - Consider the following system of...

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