Question
Verify that the equation
is integrable and find its primitive.
Answer :
Word Count : 246
We are tasked with verifying whether the equation \[ 2(y+z)dx - (x+z)dy + (2y - x + z)dz = 0 \] is integrable, and if so, finding its primitive. The equation is in the form of a first-order differential equation involving three variables: \(x\), \(y\), and \(z\). ### Step 1: Verifying Integrability For a differential equation of the form: \[ M(x, ________ ___ _____ _____ ____ _______.
_________ _____ ________ ________ ___.
_______ ___ _____ ______ _________ ________.
______ _______ _________ ____ _________ ____.
______ ___ _____ ________ ______ __________ _____ ________.
________ ______ _________ __________ ___ ____ _____ ___ ____ ____ _______ _________.
__________ ______ _____ ______ ____ _______ ______ __________.
________ __________ _____ ___ _____ __________ ______ _________ _____ _________ __________ _________.
______ ___ _____ _________ _______ ________ ______ _________ _________.
___ __________ _____ ______ _______ ___ _____ __________ ________.
______ ______ ___ _____ ____ _________ _____ _______ _________ ______.
_________ ________ ___ ________ ____ ______ ____ _______.
_________ _________ ________ _____ ______ ___ _________.
_________ ______ __________ _________ ______ __________ _________ ____ __________ ________ _________.
____ ____ ______ ___ ___ ___ ______ _______ _______.
______ _______ _____ ______ ____ _______ ______ _______.
____ _____ ____ _________ _________ _________ _______.
________ __________ __________ ____ ______ _________ ____ ________.
_________ ____ ______ _______ ______ __________.
_______ _________ _____ _______ ________ _________ _________ __________ _____ ___.
_____ _________ _____ _____ ____ _________ ___.
________ __________ _______ ______ _______ ________ ____ ________ ___ ______ _____.
____ _______.
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We are tasked with verifying whether the equation \[ 2(y+z)dx - (x+z)dy + (2y - x + z)dz = 0 \] is integrable, and if so, finding its primitive. The equation is in the form of a first-order differential equation involving three variables: \(x\), \(y\), and \(z\). ### Step 1: Verifying Integrability For a differential equation of the form: \[ M(x, ________ ___ _____ _____ ____ _______.
_________ _____ ________ ________ ___.
_______ ___ _____ ______ _________ ________.
______ _______ _________ ____ _________ ____.
______ ___ _____ ________ ______ __________ _____ ________.
________ ______ _________ __________ ___ ____ _____ ___ ____ ____ _______ _________.
__________ ______ _____ ______ ____ _______ ______ __________.
________ __________ _____ ___ _____ __________ ______ _________ _____ _________ __________ _________.
______ ___ _____ _________ _______ ________ ______ _________ _________.
___ __________ _____ ______ _______ ___ _____ __________ ________.
______ ______ ___ _____ ____ _________ _____ _______ _________ ______.
_________ ________ ___ ________ ____ ______ ____ _______.
_________ _________ ________ _____ ______ ___ _________.
_________ ______ __________ _________ ______ __________ _________ ____ __________ ________ _________.
____ ____ ______ ___ ___ ___ ______ _______ _______.
______ _______ _____ ______ ____ _______ ______ _______.
____ _____ ____ _________ _________ _________ _______.
________ __________ __________ ____ ______ _________ ____ ________.
_________ ____ ______ _______ ______ __________.
_______ _________ _____ _______ ________ _________ _________ __________ _____ ___.
_____ _________ _____ _____ ____ _________ ___.
________ __________ _______ ______ _______ ________ ____ ________ ___ ______ _____.
____ _______.
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