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 .

ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<

4th Edition

ISBN: 9781319411657

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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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

ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<

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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

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 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.