Explanation Given information: x 2 y 1 + e − y = 0 Formula used: x 2 y 1 + e − y = 0 is separable. Calculation: Consider the given differential equation. x 2 y 1 + e − y = 0 x 2 d y d x + e − y = 0 x 2 d y To determine (b) Integrate both sides to obtain e y = x − 1 + C . To determine (c) y = ln ( x − 1 + C ) is the general solution. To determine (d) The particular solution satisfying y ( 2 ) = 4 .

4th Edition

ISBN: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

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Chapter 9.1, Problem 9E

To determine

(a)

Write x2y1+e−y=0 as eydy=x2dx

To determine

(b)

Integrate both sides to obtain ey=x−1+C.

To determine

(c)

y=ln(x−1+C) is the general solution.

To determine

(d)

The particular solution satisfying y(2)=4.

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Chapter 9.1, Problem 8E

Chapter 9.1, Problem 10E

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Chapter 9 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

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(a) Write x 2 y 1 + e − y = 0 as e y d y = x 2 d x

Solution Summary: The author explains that x2y1+e-y=0 is separable.

Concept explainers

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(a)

Write x2y1+e−y=0 as eydy=x2dx

(b)

Integrate both sides to obtain ey=x−1+C.

(c)

y=ln(x−1+C) is the general solution.

(d)

The particular solution satisfying y(2)=4.

Want to see the full answer?

Chapter 9 Solutions

(a) Write x 2 y 1 + e − y = 0 as e y d y = x 2 d x

Solution Summary: The author explains that x2y1+e-y=0 is separable.

Concept explainers

Videos

(a) Write x2y1+e−y=0 as eydy=x2dx

(b) Integrate both sides to obtain ey=x−1+C.

(c) y=ln(x−1+C) is the general solution.

(d) The particular solution satisfying y(2)=4.

Want to see the full answer?

Chapter 9 Solutions

(a)

Write x2y1+e−y=0 as eydy=x2dx

(b)

Integrate both sides to obtain ey=x−1+C.

(c)

y=ln(x−1+C) is the general solution.

(d)

The particular solution satisfying y(2)=4.