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quiz_08ode_background(1) - Given the following radius of...

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08.01.1 Multiple-Choice Test Chapter 08.01 Background 1. The differential equation ( ) 5 0 , 3 2 2 2 = + = + y x y x dx dy is (A) linear (B) nonlinear (C) linear with fixed constants (D) undeterminable to be linear or nonlinear 2. A differential equation is considered to be ordinary if it has (A) one dependent variable (B) more than one dependent variable (C) one independent variable (D) more than one independent variable 3. Given ( ) 6 0 , 2 sin 3 2 = = + y x y dx dy ( ) 2 y most nearly is 4. The form of the exact solution to ( ) 5 0 , 3 2 = = + y e y dx dy x is
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08.01.2 Chapter 08.01 08.01.2 5. The following nonlinear differential equation can be solved exactly by separation of variables. ( ) ( ) 1000 0 , 81 10 2 6 = = θ θ θ dt d The value of ( ) 100 θ most nearly is 6. A solid spherical ball taken out of a furnace at 1200 K is allowed to cool in air.
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Unformatted text preview: Given the following, radius of the ball cm 2 = density of the ball 3 kg/m 7800 = specific heat of the ball K J/kg 420 ⋅ = emmittance 85 . = Stefan-Boltzman constant 4 2 8 K m J/s 10 67 . 5 ⋅ ⋅ × = − ambient temperature K 300 = convection coefficient to air K m J/s 350 2 ⋅ ⋅ = the differential equation governing the temperature of the ball as a function of time t is given by (A) ( ) 8 4 12 10 81 10 2067 . 2 × − × − = − dt d (B) ( ) 300 10 6026 . 1 2 − × − = − dt d (C) ( ) ( ) 300 10 6026 . 1 10 81 10 2067 . 2 12 8 4 12 − × + × − × = − − dt d (D) ( ) ( ) 300 10 6026 . 1 10 81 10 2067 . 2 2 8 4 12 − × − × − × − = − − dt d For a complete solution, refer to the links at the end of the book....
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