Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

What are the integrating factors for the following differential equations?$$\frac{d y}{d x}=\tanh (x) y+1$$

$\mu(x)=\frac{1}{\cosh (x)}$

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Differential Equations

Oregon State University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:58

What are the integrating f…

03:05

02:23

10:23

04:17

05:22

02:15

11:05

00:58

45 Problem number 2 21 were asked to find the integrating factor for this first order linear, ordinary differential equation. So that form is going to be D Y d X plus some function of X times y is equal to some function of X. So to get it in that form, I'm gonna have what d y d x minus the hyperbolic tangent of axe times Why is equal to one. So now you can see that p of X is this minus hyperbolic tangent of X. So my integrating factor is going to be e to the integral of p of x, the axe, the anti derivative. So this is E and in the anti derivative of minus hyperbolic tangent of X, the X And now we can go through a little bit of a simplification, the anti derivative of minus hyperbolic tangent That's minus log Hyperbolic co sign. So this is going to be e to the minus natural log of the hyperbolic co sign of X. Okay, so this is e to the natural log, um, of the hyperbolic co sign of X to the minus one, continuing with our property of exponents. This is e to the natural log of one over the hyperbolic CO sign of X and then e to the natural log of anything. So this answer is going to be one over hyperbolic co sign X. So that is the integrating factor for this particular linear, ordinary, different equation.

View More Answers From This Book

Find Another Textbook

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

What are the integrating factors for the following differential equations?

09:23

Assume an initial nutrient amount of $I$ kilograms in a tank with $L$ liters…

01:07

Evaluate $\int_{1}^{4} \frac{d x}{\sqrt{x^{2}-1}} .$ (Express the answer in …

01:48

State whether the given series converges and explain why.$1+\frac{\pi}{e…

02:10

04:16

Compute the definite integrals. Use a graphing utility to confirm your answe…

00:30

Evaluate each of the following integrals by $u$ -substitution.$$\int…

01:20

Evaluate the integrals. If the integral diverges, answer "diverges.&quo…

01:37

Draw the directional field of the threshold logistic equation, assuming $K=1…

Find a formula $a_{n}$ for the $n$ th term of the arithmetic sequence whose …

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.