Book edition 9th

Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider

Pages 616 pages

ISBN 9780321977069

Answers without the blur.

Just sign up for free and you're in.

Short Answer

In Problems 9–20, determine whether the equation is exact.
If it is, then solve it.
$(2 xy + 3) dx + (x^{2} - 1) dy = 0$

The solution is $y = (C - 3 x) / (x^{2 - 1})$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Evaluate whether the equation is exact

Here $(2 xy + 3) dx + (x^{2} - 1) dy = 0$

The condition for exact is $\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}$ .

$M (x, y) = 2 xy + 3 N (x, y) = x^{2} - 1 \frac{\partial M}{\partial y} = 2 x = 2 x = \frac{\partial N}{\partial x}$

This equation is exact.

Step 2: Find the value of F(x, y)

Here

$M (x, y) = 2 xy + 3 F (x, y) = \int M (x, y) dx + g (y) = \int (2 xy + 3) dx + g (y) = x^{2} y + 3 x + g (y)$

Step 3: Determine the value of g(y)

$\frac{\partial F}{\partial y} (x, y) = N (x, y) x^{2} + g' (y) = x^{2} - 1 g' (y) = - 1 g (y) = - y$

Now $F (x, y) = x^{2} y + 3 x - y$

$x^{2} y + 3 x - y = C (x^{2} - 1) y + 3 x = C (x^{2} - 1) y = C - 3 x y = (C - 3 x) / (x^{2} - 1)$

Therefore, the solution is $y = (C - 3 x) / (x^{2} - 1)$ $y = (C - 3 x) / (x^{2} - 1)$

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

In Problems 9–20, determine whether the equation is exact.
If it is, then solve it.
$(2 xy + 3) dx + (x^{2} - 1) dy = 0$

Step by Step Solution

Step 1: Evaluate whether the equation is exact

Step 2: Find the value of F(x, y)

Step 3: Determine the value of g(y)

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

In Problems 9–20, determine whether the equation is exact.If it is, then solve it.(2xy+3)dx+(x2-1)dy=0

Step by Step Solution

Step 1: Evaluate whether the equation is exact

Step 2: Find the value of F(x, y)

Step 3: Determine the value of g(y)

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

In Problems 9–20, determine whether the equation is exact.
If it is, then solve it.
$(2 xy + 3) dx + (x^{2} - 1) dy = 0$