Mathematics Exam > Mathematics Questions > The general integral of the partial different...
Start Learning for Free
The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 is
- a)f(x2 + y2 + z2,xy + z ) = 0
- b)f(x2 + y2 - z2,x y + z ) = 0
- c)f(x2 - y2- z2,xy + z) = 0
- d)f(x2 + y2 + z2,xy - z ) = 0
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The general integral of the partial differential equation (y + z x) zx...
To find the general integral of the partial differential equation (y z x) zx, we can integrate with respect to both x and z. Let's denote the unknown function as F(x,z):
∂F/∂x = yz + zx
Integrating both sides with respect to x:
F(x,z) = ∫ (yz + zx) dx
= yz*x + 0.5*z*x^2 + g(z)
where g(z) is an arbitrary function of z.
Now, let's differentiate F(x,z) with respect to z:
∂F/∂z = yx + g'(z)
Comparing this with the original partial differential equation, we can see that g'(z) must be equal to 0 for the equation to hold. Therefore, we can conclude that g(z) is a constant, let's call it C.
The general integral of the partial differential equation (y z x) zx is:
F(x,z) = yz*x + 0.5*z*x^2 + C
where C is an arbitrary constant.
∂F/∂x = yz + zx
Integrating both sides with respect to x:
F(x,z) = ∫ (yz + zx) dx
= yz*x + 0.5*z*x^2 + g(z)
where g(z) is an arbitrary function of z.
Now, let's differentiate F(x,z) with respect to z:
∂F/∂z = yx + g'(z)
Comparing this with the original partial differential equation, we can see that g'(z) must be equal to 0 for the equation to hold. Therefore, we can conclude that g(z) is a constant, let's call it C.
The general integral of the partial differential equation (y z x) zx is:
F(x,z) = yz*x + 0.5*z*x^2 + C
where C is an arbitrary constant.
Free Test
FREE
| Start Free Test |
Community Answer
The general integral of the partial differential equation (y + z x) zx...
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
Question Description
The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 isa)f(x2 + y2 + z2,xy + z ) = 0b)f(x2 + y2 - z2,x y + z ) = 0c)f(x2-y2-z2,xy + z) = 0d)f(x2 + y2 + z2,xy -z ) = 0Correct answer is option 'B'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 isa)f(x2 + y2 + z2,xy + z ) = 0b)f(x2 + y2 - z2,x y + z ) = 0c)f(x2-y2-z2,xy + z) = 0d)f(x2 + y2 + z2,xy -z ) = 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 isa)f(x2 + y2 + z2,xy + z ) = 0b)f(x2 + y2 - z2,x y + z ) = 0c)f(x2-y2-z2,xy + z) = 0d)f(x2 + y2 + z2,xy -z ) = 0Correct answer is option 'B'. Can you explain this answer?.
The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 isa)f(x2 + y2 + z2,xy + z ) = 0b)f(x2 + y2 - z2,x y + z ) = 0c)f(x2-y2-z2,xy + z) = 0d)f(x2 + y2 + z2,xy -z ) = 0Correct answer is option 'B'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 isa)f(x2 + y2 + z2,xy + z ) = 0b)f(x2 + y2 - z2,x y + z ) = 0c)f(x2-y2-z2,xy + z) = 0d)f(x2 + y2 + z2,xy -z ) = 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 isa)f(x2 + y2 + z2,xy + z ) = 0b)f(x2 + y2 - z2,x y + z ) = 0c)f(x2-y2-z2,xy + z) = 0d)f(x2 + y2 + z2,xy -z ) = 0Correct answer is option 'B'. Can you explain this answer?.
Solutions for The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 isa)f(x2 + y2 + z2,xy + z ) = 0b)f(x2 + y2 - z2,x y + z ) = 0c)f(x2-y2-z2,xy + z) = 0d)f(x2 + y2 + z2,xy -z ) = 0Correct answer is option 'B'. 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 general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 isa)f(x2 + y2 + z2,xy + z ) = 0b)f(x2 + y2 - z2,x y + z ) = 0c)f(x2-y2-z2,xy + z) = 0d)f(x2 + y2 + z2,xy -z ) = 0Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 isa)f(x2 + y2 + z2,xy + z ) = 0b)f(x2 + y2 - z2,x y + z ) = 0c)f(x2-y2-z2,xy + z) = 0d)f(x2 + y2 + z2,xy -z ) = 0Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 isa)f(x2 + y2 + z2,xy + z ) = 0b)f(x2 + y2 - z2,x y + z ) = 0c)f(x2-y2-z2,xy + z) = 0d)f(x2 + y2 + z2,xy -z ) = 0Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 isa)f(x2 + y2 + z2,xy + z ) = 0b)f(x2 + y2 - z2,x y + z ) = 0c)f(x2-y2-z2,xy + z) = 0d)f(x2 + y2 + z2,xy -z ) = 0Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The general integral of the partial differential equation (y + z x) zx — (x + yz)Zy = x2 — y2 isa)f(x2 + y2 + z2,xy + z ) = 0b)f(x2 + y2 - z2,x y + z ) = 0c)f(x2-y2-z2,xy + z) = 0d)f(x2 + y2 + z2,xy -z ) = 0Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup