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# Differential Equations

# Differential Equations: Give Me a Solution, I'll Give You an Answer Quiz

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Differential Equations**Q. Which of the following is not a differential equation?

*y*' = 0

*x*

^{2}+

*xy*= 6 -

*y*

^{2}

*f*

^{(2)}(

*x*) =

*f*(

*x*) -

*x*

^{2}

Q. Determine the order of the differential equation

*f*^{4}(*x*) +*f*^{(2)}(*x*) = 5 -*f*^{(3)}(*x*) +*f*(*x*)1

2

3

4

Q. A

*solution*to a differential equation isa function that satisfies that differential equation.

a number that satisfies that differential equation.

a function that satisfies that differential equation and some additional constraint.

the highest derivative in that differential equation.

Q. The function

*y* = *x*^{2}

is a solution to which one of the following differential equations?

2

*y*=*y*'*y*' = 2

*y*"

*y*=

*xy*'

2

*y*=*xy*'Q. Determine which of the following functions is NOT a solution to the d.e.

*f*^{(2)}(*x*) = -*f*(*x*).*f*(

*x*) = 0

*f*(

*x*) = sin

*x*

*f*(

*x*) = -cos

*x*

*f*(

*x*) = -

*e*

^{ - x}

Q. Determine which of the following functions is a solution to the IVP

*y*" =*y*and*y*(0) = 1.*y*= 0

*y*= 1

*y*=

*e*

^{-x}

*y*= -

*e*

^{-x}

Q. Determine which of the following is the particular solution to the IVP

*y*" = 8.*y*= 4

*x*

^{2}+

*B*

*x*+

*C*

*y*= 4

*x*

^{2}- 8

*x*+ 1

*B*= -8 and

*C*= 1

*y*' = 8

*x*- 8

Q. Determine which differential equation best represents the following English statement:

The monkey population is increasing at a rate of 1 percent.

Q. Julianna spends 20 per week. If M represents Julianna's money and

*t*represents time measured in years, which differential equation best describes this situation?Q. A family of rabbits has a birth rate of 25 percent. Every year 10 rabbits die. Which of the following differential equations best models this situation?