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

Solve the following initial-value problems by using integrating factors.$$y^{\prime}=x y+2 x e^{x}, y(0)=2$$

$y(x)=4 e^{x^{2} / 2}-2 e^{x}+\sqrt{\frac{\pi e}{2}} e^{1 / 2}\left(\operatorname{erf}\left(\frac{-1}{2}\right)-\operatorname{erf}\left(\frac{x-1}{2}\right)\right) e^{x^{2} / 2}$

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Differential Equations

Missouri State University

Oregon State University

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

03:23

Solve the following initia…

04:20

03:44

03:48

05:25

03:03

02:02

02:36

04:29

Solve the initial value pr…

01:43

Israel. We are going to solve this differential equation. Why? Prime minus two y equal x times e to the X with initial condition that X equals zero give Why equal minus one. Okay, um so it is stand out. Form P of X is just minus two. Integrating factor would be e to the minus two x We multiply this true left hand side going to become Why times e to the minus two x Oh, this primes equals right hand side will be here will be e to the minus X now And we have to integrate the right hands I So we use it to grow by past again. You is just x Do you is e to minus x d X Now the U is the X and we will be minus E to the minus eggs. Put everything in the formula we get, um to the end. It will be this. So this should be where if you should be very familiar with this technique already, and the term that you see Owen over like x time e to there's something should be to it too hard. So practice. Ah, we put this in back in here, and I'm gonna skip to what? Why? Looks like here. So we shared from E to the minus to the, uh, plus X now, because we we used to have even a mite has two x on the left side. And like we calculate it out, we get this general solution. Now, we put in the condition here. Why is minus one when x is zero? So is zero minus one plus c. So the sea is actually Ciro this term gonna disappear and yeah, why will be just this, um, I thing You can pull this out. Yeah. Um sorry. Let me shake. Yes is correct. Uh, this is Thea Answer. There's no constant yet because C is zero. That is the answer. Thank you.

View More Answers From This Book

Find Another Textbook

Numerade Educator

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…

Solve the following initial-value problems by using integrating factors.…

Solve the initial value problems.\begin{equation}\frac{d^{2} y}{d x^{2}}…

Solve the following initial value problems.$$y^{\prime}(x)=-y+2, y(0)=-2…

02:13

For each of the following series, use the sequence of partial sums to determ…

03:57

Use the given substitution to convert the integral to an integral of a ratio…

01:54

Find a function $f(n)$ that identifies the $n$ th term $a_{n}$ of the follow…

05:24

For the following problems, use Newton’s law of cooling.You have a cup o…

02:00

For each of the following sequences, whose $n$th terms are indicated, state …

00:47

Determine the limit of the sequence or show that the sequence diverges. If i…

03:14

Estimate the following solutions using Euler's method with $n=5$ steps …

01:36

Graph the curve $y=\frac{x}{1+x}$ over the interval $[0,5] .$ Then, find the…

00:50

Suppose that $$\sum_{n=1}^{\infty} a_{n}=1,$$ that $$\sum_{n=1}^{\infty} b_{…

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.