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Evaluate the following differential equations: a) Variable Separable/Homogeneous Equation (x-y iny+y ln x) dx +x (In y-In x) dy = 0

Evaluate the following differential equations: a) Variable Separable/Homogeneous Equation (x-y iny+y ln x) dx +x (In y-In x) dy = 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Evaluate the following differential equations:
a) Variable Separable/Homogeneous Equation
(x − y ln y + y ln x)dx + x(ln y − ln x)dy = 0

b) Integrating Factor by Formula
1. (2y^2 + 2y + 4x2)dx + (2xy + x)dy = 0

2. y^2cos xdx + (4 + 5y sin x)dy = 0

c) Bernoulli’s Equation
xdy − ydx − xy^3dx − xy^3 ln xdx = 0

d) Use Substitution method

y′tan x sin 2y = sin2 x + cos2y

Evaluate the following differential equations: a) Variable Separable/Homogeneous Equation (x-y Iny+y ln x) dx +x (In y-In x) dy =0 b) Integrating Factor by Formula 1. (2y^2 2y 4x2) dx + (2xy + x) dy 0 2. y^2cos xdx+ (4 Sy sin sinx) dy = 0 ) Bernoulli's Equation d) Use Substitution method y tan x sin 2y= sin^2x cos 2y
Transcribed Image Text:Evaluate the following differential equations: a) Variable Separable/Homogeneous Equation (x-y Iny+y ln x) dx +x (In y-In x) dy =0 b) Integrating Factor by Formula 1. (2y^2 2y 4x2) dx + (2xy + x) dy 0 2. y^2cos xdx+ (4 Sy sin sinx) dy = 0 ) Bernoulli's Equation d) Use Substitution method y tan x sin 2y= sin^2x cos 2y
Evaluate the following differential equations: a) Variable Separable/Homogeneous Equation (x-y Iny+y ln x) dx +x (In y-In x) dy =0 b) Integrating Factor by Formula 1. (2y^2 2y 4x2) dx + (2xy + x) dy 0 2. y^2cos xdx+ (4 Sy sin sinx) dy = 0 ) Bernoulli's Equation d) Use Substitution method y tan x sin 2y= sin^2x cos 2y
Transcribed Image Text:Evaluate the following differential equations: a) Variable Separable/Homogeneous Equation (x-y Iny+y ln x) dx +x (In y-In x) dy =0 b) Integrating Factor by Formula 1. (2y^2 2y 4x2) dx + (2xy + x) dy 0 2. y^2cos xdx+ (4 Sy sin sinx) dy = 0 ) Bernoulli's Equation d) Use Substitution method y tan x sin 2y= sin^2x cos 2y
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