Mathematics Exam > Mathematics Questions > The integral surface of the p. d. esatisfying...
Start Learning for Free
The integral surface of the p. d. e 
satisfying the condition u ( 1 , y ) = y is given by
satisfying the condition u ( 1 , y ) = y is given by- a)u(x,y) = y/x
- b)u(x, y) =
- c)u(x, y)
- d)u(x,y) = y + x - 1
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The integral surface of the p. d. esatisfying the condition u ( 1 , y ...
Think of the PDE as ∇u⋅(a(x,y),b(x,y))=0∇u⋅(a(x,y),b(x,y))=0 so that, geometrically it must be that dy/dx = [b(x,y)/a(x,y)] The solution of the ODE defines the characteristic curves of the PDE, along which solutions (to the PDE) are constant. Then u(x,y) = f(C) where the function ff is determined from the given auxiliary condition.
For example, here the ODE is dy/dx = y/x
so C = ln|y/x|
Then u(x,y) = f(C) = f(ln|y/x|).
To determine f, apply the given condition: u(1,y) = f(ln|y|) = y
⟹ f(y) = ey
Thus, u(x,y) = exp(ln|y/x|)
= |y/x|
Most Upvoted Answer
The integral surface of the p. d. esatisfying the condition u ( 1 , y ...
Think of the PDE as ∇u⋅(a(x,y),b(x,y))=0∇u⋅(a(x,y),b(x,y))=0 so that, geometrically it must be that dy/dx = [b(x,y)/a(x,y)] The solution of the ODE defines the characteristic curves of the PDE, along which solutions (to the PDE) are constant. Then u(x,y) = f(C) where the function ff is determined from the given auxiliary condition.
For example, here the ODE is dy/dx = y/x
so C = ln|y/x|
Then u(x,y) = f(C) = f(ln|y/x|).
To determine f, apply the given condition: u(1,y) = f(ln|y|) = y
⟹ f(y) = ey
Thus, u(x,y) = exp(ln|y/x|)
= |y/x|
|
Explore Courses for Mathematics exam
|
|
The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer?
Question Description
The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer?.
The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer?.
Solutions for The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The integral surface of the p. d. esatisfying the condition u ( 1 , y ) = y is given bya)u(x,y) = y/xb)u(x, y) =c)u(x, y)d)u(x,y) = y + x - 1Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup