/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q9E In Problems 9鈥�20, determine wh... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q9E (page 1)

In Problems 9鈥�20, determine whether the equation is exact.

If it is, then solve it.

(2xy+3)dx+(x2-1)dy=0

Short Answer

Expert verified

The solution isy=C-3x/x2-1.

Step by step solution

01

Evaluate whether the equation is exact

Here(2xy+3)dx+(x2-1)dy=0

The condition for exact is鈭�M鈭�y=鈭�N鈭�x .

M(x,y)=2xy+3N(x,y)=x2-1鈭�M鈭�y=2x=2x=鈭�N鈭�x

This equation is exact.

02

Find the value of F(x, y)

Here

M(x,y)=2xy+3F(x,y)=鈭�M(x,y)dx+g(y)=鈭�(2xy+3)dx+g(y)=x2y+3x+g(y)

03

Determine the value of g(y)

鈭�F鈭�y(x,y)=N(x,y)x2+g'(y)=x2-1g'(y)=-1g(y)=-y

NowF(x,y)=x2y+3x-y

x2y+3x-y=C(x2-1)y+3x=C(x2-1)y=C-3xy=(C-3x)/(x2-1)

Therefore, the solution isy=(C-3x)/(x2-1)y=(C-3x)/(x2-1)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Problems 9鈥�13, determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship implicitly defines y as a function of x and use implicit differentiation.

exy+y=x-1,dydx=e-xy-ye-xy+x

Consider the differential equation dydx=x+siny

猞� A solution curve passes through the point (1,蟺2). What is its slope at this point?

猞� Argue that every solution curve is increasing for x>1.

猞� Show that the second derivative of every solution satisfies d2ydx2=1+xcosy+12sin2y.

猞� A solution curve passes through (0,0). Prove that this curve has a relative minimum at (0,0).

The direction field for dydx=2x+yas shown in figure 1.13.

  1. Sketch the solution curve that passes through (0, -2). From this sketch, write the equation for the solution.

b. Sketch the solution curve that passes through (-1, 3).

c. What can you say about the solution in part (b) as x鈫�+鈭�? How about x鈫�-鈭�?

Question:Use a CAS to graphJ3/2(x),J-3/2(x),J5/2(x), and J-5/2(x).

The logistic equation for the population (in thousands) of a certain species is given by dpdt=3p-2p2.

猞� Sketch the direction field by using either a computer software package or the method of isoclines.

猞� If the initial population is 3000 [that is, p(0) = 3], what can you say about the limiting population?

猞� If p(0)=0.8, what is limt鈫�+鈭�p(t)?

猞� Can a population of 2000 ever decline to 800?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.