Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Verify that the following functions are solutions to the given differential equation.$y=e^{x^{2} / 2}$ solves $y^{\prime}=x y$

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Taylor Shimono

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 1

Basics of Differential Equations

Differential Equations

Missouri State University

Campbell University

Oregon State University

Baylor University

Lectures

13:37

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

33:32

01:13

Verify that the following …

02:15

02:00

02:22

00:49

So because of the fact that our differential equation involves a Y prime, the first step in solving this problem is going to be finding the first derivative of why So why prime is going to be equal to We're gonna have to do the chain well here. So, first we'll take the derivative of X squared over two and using the power rule, we know that this is going to be two x to the first power over to and this will be times E to the same exponents, um X squared over two. And so when we simplify, we find that why Prime is equal to X e the X squared over two. And so when we substitute of this into our differential equation, we know that Ah, why prime again is X e to the X squared over too. And this should be equal to X times. Why? And so we know that why is equal to e to the X squared over two. So when we plug all this into our differential equation, we get X E to the X squared over two is equal to x e to the x squared over to power. So since he's a reek willl that tells us that why is a solution to

View More Answers From This Book

Find Another Textbook

05:04

16.Find the angle a rafter makes with the joist of a house if the rise o…

04:15

QUESTION 12pointsSave AnswerThe number showing on the upper face…

03:11

Solve the system using either Gaussian elimination with back- substitution o…

02:51

(c) The symmetric middle area on a N (10,5) curve is about 0.95_Round yo…

03:54

How many different spanning trees does the following graph have?

03:22

Circulation, Curl Form of Green's Theorem 6. Consider the vector field …

03:49

Use a system of equations to solve the following problem_How many ounces…

02:34

The random variable X takes values -1 , 0, with probabilities 1/8, 2/8, 5/8 …

02:23

A random sample of specific brand of snack bar is tested for calorie count; …

05:28

point) According to U.S postal regulations the girth plus the length of a pa…