Differential Equations and Integrals

Differential Equations and Integrals

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
7.EE.A.1, HSA-REI.B.4B

Standards-aligned

Created by

Ethan Morris

FREE Resource

Standards-aligned

CCSS.7.EE.A.1
,
CCSS.HSA-REI.B.4B
The video tutorial explains how to solve a separable differential equation using an initial condition. It begins by introducing the problem and rearranging the equation to separate variables. The process involves integrating both sides to find the general solution and then using the initial condition to determine the particular solution. The tutorial provides a step-by-step approach to solving the equation, emphasizing the importance of integration and constant determination.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial condition given in the problem?

y(1) = 2

y(3) = 4

y(0) = 1

y(2) = 3

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What type of differential equation is being solved?

Homogeneous

Non-linear

Linear

Separable

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in solving the given differential equation?

Add a constant to both sides

Multiply both sides by dx

Divide both sides by y

Divide both sides by x

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the form of the equation after separating variables?

dy/dx = (1/x + 1) y^6

y^6 dy = (1 + x) dx

y^6 dy = (1/x + 1) dx

dy/dx = y^6 (1 + x)

Tags

CCSS.7.EE.A.1

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the integral of y^6 with respect to y?

6y^7

y^6/6

7y^6

y^7/7

Tags

CCSS.7.EE.A.1

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the integral of 1/x with respect to x?

1/x

x

x^2/2

ln|x|

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the constant of integration determined?

By setting it to zero

By differentiating the solution

By using the initial condition

By integrating again

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