Differential Equations Concepts Review

Differential Equations Concepts Review

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Hard

CCSS
HSF.IF.A.2

Standards-aligned

Created by

Olivia Brooks

FREE Resource

Standards-aligned

CCSS.HSF.IF.A.2
This video tutorial explains how to solve a linear first-order differential equation using an integrating factor. It covers ensuring the equation is in the correct form, finding the integrating factor, multiplying the equation by this factor, and integrating both sides to solve for y. The tutorial also demonstrates using integration by parts to solve complex integrals, ultimately leading to the general solution of the differential equation.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the correct form of a linear first order differential equation?

dy/dt - P(t) * y = F(t)

dy/dt + P(t) * y = F(t)

dy/dt = P(t) * y + F(t)

dy/dt + y = P(t) * F(t)

Tags

CCSS.HSF.IF.A.2

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the given equation, what is the value of P(t)?

2

3

5

4

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the integrating factor μ(t) determined?

By calculating e raised to the integral of P(t)

By differentiating P(t)

By integrating F(t)

By multiplying P(t) and F(t)

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of multiplying the differential equation by the integrating factor?

To eliminate the constant term

To transform the equation into a derivative of a product

To simplify the equation

To find the value of y

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which rule is applied to check the derivative of the product on the left side?

Product rule

Quotient rule

Power rule

Chain rule

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What method is used to evaluate the integral on the right side of the equation?

Integration by parts

Trigonometric substitution

Partial fractions

Substitution

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in integration by parts?

Multiply U and V

Choose U and differentiate it

Integrate U

Differentiate V

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