Understanding First Order Linear Differential Equations

Understanding First Order Linear Differential Equations

Assessment

Interactive Video

Mathematics

11th - 12th Grade

Practice Problem

Hard

Created by

Jennifer Brown

FREE Resource

10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the defining characteristic of a first order linear differential equation?

It can be written in the form y' + p(x)y = q(x).

It includes a second derivative.

It is always non-linear.

It has a constant solution.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the first example, what is the integrating factor used?

e^(2x)

e^(-2x)

e^(x)

e^(-x)

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why do we multiply the differential equation by the integrating factor?

To transform the left side into a product rule form.

To eliminate the derivative.

To make the equation non-linear.

To simplify the equation to a constant.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What substitution is used in the integration process of the first example?

u = 2x

u = -2x

u = x

u = -x

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the general solution form for the first example?

y = -3 + e^(2x)

y = -3 + c * e^(2x)

y = 3 + c * e^(2x)

y = 3 + e^(2x)

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the second example, what transformation is applied to the equation initially?

Dividing by x

Adding a constant

Multiplying by x

Subtracting a constant

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the integrating factor for the second example?

1/x

e^(-x)

x

e^(x)

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