Differential Equations Quiz

What is a differential equation?

• An equation with no variables

• An equation that cannot be solved

• An equation involving only constants

• An equation involving a derivative

What determines the order of a differential equation?

• The number of variables

• The highest power of the variable

• The number of constants

• The highest derivative involved

In the example dydx = 4x^2 - 3x + 2, what is the order of the differential equation?

• Third

• Second

• Zero

• First

What is the method used to solve the first example of a first-order differential equation?

• Integration by parts

• Separation of variables

• Partial fraction decomposition

• Laplace transform

In the first example, what is the integral of the right side of the equation?

• X^2 + C

• X^4 + C

• X^3 + C

• X + C

In the second example, what is the initial condition given?

• y(0) = 0

• y(1) = 12

• y(2) = 5

• y(3) = 7

What is the final form of the solution in the second example?

• Y = 12 e^2x + 3x^2 + C

• Y = 12 e^2x - 3x^2 + 2 - e^2/2

• Y = 12 e^2x - 3x^2 + C

• Y = 12 e^2x - 3x^2 - 2 + e^2/2

What is the order of the differential equation in the third example?

• First

• Second

• Third

• Fourth

In the third example, what is the initial condition for the derivative?

• y'(2) = 2

• y'(0) = 0

• y'(3) = 3

• y'(1) = 1

What is the final solution for y in the third example?

• y = 1/5 x^3 + 5/5

• y = 1/4 x^3 + 5/4

• y = 1/2 x^3 + 5/2

• y = 1/3 x^3 + 5/3