# Quiz Chapter 08.01 Primer for Ordinary Differential Equations

 MULTIPLE CHOICE TEST BACKGROUND ORDINARY DIFFERENTIAL EQUATIONS

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 $1200$K 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 $=300$K
• 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