Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. For the given Lie group, find the corresponding infinitesimals X and Y. (i) x=coshex+sinhey, y=coshey+sinh Ex (ii) =√√x²-2y+2yeε, y = yeε, (iii) x=x √1+2E12 y = y √1+2ɛy2 2. For the given infinitesimals X and Y, find the corresponding Lie group. (i) x=xy, Y=1 (ii) X=x+y, Y = y, (iii) X = x²-x, Y = y² + y. 3. Find infinitesimal transformations leaving the following ODEs invari- ant. Use these to find a change of variables and reduce the original ODE to one that is separable and solve the equation. (i) (ii) ** ** dy = xy + dx x xy al× dy (iii) = dx dy dx = 3y + 2y+x3 y+y³ x+(x+1)y² Hints: Try: 1. X = 4(x), Y = B(x)y, 2. X=A(x), Y = B(y), 3. X = 4(y), Y = B(x).

1. For the given Lie group, find the corresponding infinitesimals X and Y. (i) x=coshex+sinhey, y=coshey+sinh Ex (ii) =√√x²-2y+2yeε, y = yeε, (iii) x=x √1+2E12 y = y √1+2ɛy2 2. For the given infinitesimals X and Y, find the corresponding Lie group. (i) x=xy, Y=1 (ii) X=x+y, Y = y, (iii) X = x²-x, Y = y² + y. 3. Find infinitesimal transformations leaving the following ODEs invari- ant. Use these to find a change of variables and reduce the original ODE to one that is separable and solve the equation. (i) (ii) ** ** dy = xy + dx x xy al× dy (iii) = dx dy dx = 3y + 2y+x3 y+y³ x+(x+1)y² Hints: Try: 1. X = 4(x), Y = B(x)y, 2. X=A(x), Y = B(y), 3. X = 4(y), Y = B(x).

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter6: Equations
Section: Chapter Questions
Problem 5GP
See similar textbooks
icon
Related questions
Question

Solve pass to pass

1. For the given Lie group, find the corresponding infinitesimals X and Y. (i) x=coshex+sinhey, y=coshey+sinh Ex (ii) =√√x²-2y+2yeε, y = yeε, (iii) x=x √1+2E12 y = y √1+2ɛy2 2. For the given infinitesimals X and Y, find the corresponding Lie group. (i) x=xy, Y=1 (ii) X=x+y, Y = y, (iii) X = x²-x, Y = y² + y. 3. Find infinitesimal transformations leaving the following ODEs invari- ant. Use these to find a change of variables and reduce the original ODE to one that is separable and solve the equation. (i) (ii) ** ** dy = xy + dx x xy al× dy (iii) = dx dy dx = 3y + 2y+x3 y+y³ x+(x+1)y² Hints: Try: 1. X = 4(x), Y = B(x)y, 2. X=A(x), Y = B(y), 3. X = 4(y), Y = B(x).
Transcribed Image Text:1. For the given Lie group, find the corresponding infinitesimals X and Y. (i) x=coshex+sinhey, y=coshey+sinh Ex (ii) =√√x²-2y+2yeε, y = yeε, (iii) x=x √1+2E12 y = y √1+2ɛy2 2. For the given infinitesimals X and Y, find the corresponding Lie group. (i) x=xy, Y=1 (ii) X=x+y, Y = y, (iii) X = x²-x, Y = y² + y. 3. Find infinitesimal transformations leaving the following ODEs invari- ant. Use these to find a change of variables and reduce the original ODE to one that is separable and solve the equation. (i) (ii) ** ** dy = xy + dx x xy al× dy (iii) = dx dy dx = 3y + 2y+x3 y+y³ x+(x+1)y² Hints: Try: 1. X = 4(x), Y = B(x)y, 2. X=A(x), Y = B(y), 3. X = 4(y), Y = B(x).
Expert Solution
steps

Step by step

Solved in 2 steps with 32 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS