Quiz Chapter 08.01 Primer for Ordinary Differential Equations

MULTIPLE CHOICE TEST

(All Tests)

BACKGROUND

(More on Ordinary Differential Equations)

ORDINARY DIFFERENTIAL EQUATIONS

(More on Ordinary Differential Equations)

Pick the most appropriate answer

1. The differential equation 2 \dfrac{dy}{dx} + x^{2}y = 2x + 3, \, y(0) = 5 is

 
 
 
 

2. A differential equation is considered to be ordinary if it has

 
 
 
 

3. Given

      • 2 \dfrac{dy}{dx} + 3y = \sin 2x, \, y(0) = 6,

y(2) is most nearly

 
 
 
 

4. The form of the exact solution to 2 \dfrac{dy}{dx} + 3y = e^{-x}, \, y(0) = 5 is

 
 
 
 

5. The following nonlinear differential equation can be solved exactly by separation of variables.

      • \dfrac{d \theta}{dt} = -10^{-6} \left( \theta^{2} - 81 \right), \, \theta(0) = 1000

The value of \theta (100) is most nearly

 
 
 
 

6. A spherical solid ball taken out of a furnace at 1200K is allowed to cool in air. Given the following:

      • radius of ball =2 cm
      • density of ball =7800 kg/m3
      • specific heat of ball =420 J/(kg-K)
      • emmittance =0.85
      • Stefan-Boltzman constant =5.67 \times 10^{-8} J/(s-m2-K4)
      • ambient temperature =300K
      • convection coefficient to air =350 J/(s-m2-K)

The differential equation governing the temperature, \theta, of the ball as a function of time is given by