mock final

mock final - ENGR 232 Dynamic Engineering Systems:Mock...

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Unformatted text preview: ENGR 232 Dynamic Engineering Systems:Mock Final 1 1. Solve the following first-order differential equa- tions: (a) (1- x 3 ) dy dx = 3 x 2 y (b) t 3 y + 4 t 2 y = e- t , y (- 1) = 0 (c) dy dx = xy 2- x- y 2 +1 xy- 3 y +2 x- 6 (d) ( x 3- y 3 ) dx- 2 x 2 ydy = 0 (e) (1 + e x ) dy dx + e x y = 0 (f) cosx dy dx + ysinx = 1 2. For the following system of two first-order differ- ential equations, determine the Eigen Values Corresponding eigen vectors General Solutions Constants subject to the initial conditions (a) dx dt =- 1 1- 4 x , x(0) = 2 3 (b) dx dt = 1 1 4 1 x , x(0) = 4 6 (c) dx dt = 3- 2 4- 1 x 3. Transform the following second order differen- tial equations to a system of first order differen- tial equations. Find the solution by determining the Eigen values and corresponding eigen vec- tors, the general solution and the value of the constants based on the initial conditions (a) y 00- 2 y- 3 y = 0, y (0) = 1, y (0) = 0 (b) y 00 + 4 y = 0, y (0) = 1, y (0) =- 2 4. A large tank is filled with 500 gallons of pure4....
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mock final - ENGR 232 Dynamic Engineering Systems:Mock...

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