SOLUTION MANUAL
Advanced Engineering Mathematics | 8th Edition
By Peter V. O'Neil
LU
XE
LI
BR
AR
Y
, TABLE OF CONTENT
Part 1: Ordinary Differential Equations
Chapter 1: First-Order Differential Equations
Chapter 2: Second-Order Differential Equations
Chapter 3: The Laplace Transform
Chapter 4: Sturm-Liouville Problems and Eigenfunction Expansions
Part 2: Partial Differential Equations
Chapter 5: The Heat Equation
Chapter 6: The Wave Equation
LU
Chapter 7: Laplace’s Equation
Chapter 8: Special Functions and Applications
Chapter 9: Transform Methods of Solution
Part 3: Matrices and Linear Algebra
Chapter 10: Vectors and the Vector Space R^n
XE
Chapter 11: Matrices, Determinants, and Linear Systems
Chapter 12: Eigenvalues, Diagonalization, and Special Matrices
Part 4: Systems of Differential Equations
Chapter 13: Systems of Linear Differential Equations
LI
Chapter 14: Nonlinear Systems and Qualitative Analysis
Part 5: Vector Analysis
Chapter 15: Vector Differential Calculus
BR
Chapter 16: Vector Integral Calculus
Part 6: Fourier Analysis
Chapter 17: Fourier Series
Chapter 18: Fourier Transforms
Part 7: Complex Functions
AR
Chapter 19: Complex Numbers and Functions
Chapter 20: Integration
Chapter 21: Series Representations of Functions
Chapter 22: Singularities and the Residue Theorem
Chapter 23: Conformal Mappings
Y
, vi CONTENTS
Chapter 1
LU
First-Order Differential
Equations
XE
1.1 Terminology and Separable Equations
1. The differential equation is separable because it can be written
LI
dy
3y2 = 4x,
dx
or, in differential form,
BR
3y2 dy = 4xdx.
Integrate to obtain
y3 = 2x2 + k.
This implicitly defines a general solution, which can be written explicitly
as
AR
y = (2x2 + k)1/3,
with k an arbitrary constant.
3. If cos(y) /= 0, the differential equation is
y sin(x + y)
=
dx cos(y)
Y
sin(x) cos(y) + cos(x) sin(y)
=
cos(y)
= sin(x) + cos(x) tan(y).
There is no way to separate the variables in this equation, so the differen-
tial equation is not separable.
1
© 2018 Cengage Learning. All Rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, LU
XE
LI
BR
AR
Y
Advanced Engineering Mathematics | 8th Edition
By Peter V. O'Neil
LU
XE
LI
BR
AR
Y
, TABLE OF CONTENT
Part 1: Ordinary Differential Equations
Chapter 1: First-Order Differential Equations
Chapter 2: Second-Order Differential Equations
Chapter 3: The Laplace Transform
Chapter 4: Sturm-Liouville Problems and Eigenfunction Expansions
Part 2: Partial Differential Equations
Chapter 5: The Heat Equation
Chapter 6: The Wave Equation
LU
Chapter 7: Laplace’s Equation
Chapter 8: Special Functions and Applications
Chapter 9: Transform Methods of Solution
Part 3: Matrices and Linear Algebra
Chapter 10: Vectors and the Vector Space R^n
XE
Chapter 11: Matrices, Determinants, and Linear Systems
Chapter 12: Eigenvalues, Diagonalization, and Special Matrices
Part 4: Systems of Differential Equations
Chapter 13: Systems of Linear Differential Equations
LI
Chapter 14: Nonlinear Systems and Qualitative Analysis
Part 5: Vector Analysis
Chapter 15: Vector Differential Calculus
BR
Chapter 16: Vector Integral Calculus
Part 6: Fourier Analysis
Chapter 17: Fourier Series
Chapter 18: Fourier Transforms
Part 7: Complex Functions
AR
Chapter 19: Complex Numbers and Functions
Chapter 20: Integration
Chapter 21: Series Representations of Functions
Chapter 22: Singularities and the Residue Theorem
Chapter 23: Conformal Mappings
Y
, vi CONTENTS
Chapter 1
LU
First-Order Differential
Equations
XE
1.1 Terminology and Separable Equations
1. The differential equation is separable because it can be written
LI
dy
3y2 = 4x,
dx
or, in differential form,
BR
3y2 dy = 4xdx.
Integrate to obtain
y3 = 2x2 + k.
This implicitly defines a general solution, which can be written explicitly
as
AR
y = (2x2 + k)1/3,
with k an arbitrary constant.
3. If cos(y) /= 0, the differential equation is
y sin(x + y)
=
dx cos(y)
Y
sin(x) cos(y) + cos(x) sin(y)
=
cos(y)
= sin(x) + cos(x) tan(y).
There is no way to separate the variables in this equation, so the differen-
tial equation is not separable.
1
© 2018 Cengage Learning. All Rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, LU
XE
LI
BR
AR
Y
