Differential Equations and Integrals

Differential Equations and Integrals

Assessment

Interactive Video

Mathematics

11th Grade - University

Practice Problem

Hard

CCSS
HSA.REI.C.7

Standards-aligned

Created by

Lucas Foster

FREE Resource

Standards-aligned

CCSS.HSA.REI.C.7
This video tutorial explains how to solve an exact first-order differential equation. It begins by introducing the form of exact differential equations and the conditions for exactness. The tutorial then verifies the exactness of a given equation by comparing partial derivatives. It proceeds to find the solution by integrating with respect to x and discusses the inclusion of a function of y. Finally, it compares the derived function with the original equation to finalize the solution, concluding with the solution form.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a necessary condition for a differential equation to be considered exact?

The equation must be linear.

The equation must be homogeneous.

The partial of M with respect to x must equal the partial of N with respect to y.

The partial of M with respect to y must equal the partial of N with respect to x.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the given differential equation, what is the expression for M(x, y)?

2e^(2x) cos(y) - 4y^2 cos(2x)

2e^(2x) sin(y) - 4y^2 sin(2x)

e^(2x) cos(y) + 4y cos(2x)

e^(2x) sin(y) + 4y sin(2x)

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you verify that a differential equation is exact?

By checking if the equation is linear.

By ensuring the partial derivatives of M and N with respect to x and y are equal.

By checking if the equation is homogeneous.

By solving the equation directly.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the form of the solution for an exact differential equation?

f(x, y) = xy

f(x, y) = c

f(x, y) = 0

f(x, y) = x + y

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When integrating M with respect to x, what must be included?

A function of y

A constant

A function of x

A function of both x and y

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What substitution is used during the integration process?

u = 2x

u = 2y

u = y

u = x

Tags

CCSS.HSA.REI.C.7

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of integrating e^(2x) sin(y) with respect to x?

e^(2x) sin(y)

2e^(2x) sin(y)

e^(2x) cos(y)

2e^(2x) cos(y)

Tags

CCSS.HSA.REI.C.7

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