Differential Equations Quiz

What are the three main classes of first-order differential equations introduced in the tutorial?

• Separable, linear, and quadratic

• Linear, quadratic, and cubic

• Separable, linear, and exact

• Exact, quadratic, and cubic

What is a homogeneous function in the context of differential equations?

• A function that is linear

• A function that is constant

• A function where scaling the arguments scales the function by a power of the parameter

• A function that is always zero

How can you identify a homogeneous differential equation?

• It is always separable

• It is always linear

• It can be written in terms of a single variable

• It involves functions that are homogeneous of the same order

What substitution is used to solve a homogeneous differential equation?

• y = u + x

• y = u * x

• y = x / u

• y = u - x

In the example provided, what is the form of the differential equation that indicates it is homogeneous?

• dy/dx = x/y

• dy/dx = x + y

• dy/dx = x^2 + y^2 / xy

• dy/dx = x^2 - y^2

What is the key characteristic of a Bernoulli differential equation?

• It has no constant terms

• It is always linear

• It has a term with y raised to a power

• It is always separable

What substitution is used to solve a Bernoulli differential equation?

• u = y^(n-1)

• u = y^n

• u = y^(1-n)

• u = y^(1+n)

In the Bernoulli DE example, what is the value of n?

• 6

• 7

• 8

• 5

What is the general solution form for the Bernoulli DE example provided?

• y = (1 - k * e^(x^6))^(-1/6)

• y = (1 + k * e^(x^6))^(-1/6)

• y = 1 - k * e^(x^6)

• y = 1 + k * e^(x^6)

What is the best way to become proficient in identifying and solving different types of differential equations?

• Memorizing formulas

• Practicing regularly

• Reading textbooks

• Watching videos