Question
हल कीजिए : .
Answer :
Word Count : 581
__________ ________ _____ _____ _________ ____ ____ ______ _______ ___ _______ __________.
________ ________ _________ __________ ______ _______ _________ _________ ___.
_____ ____ ________ _____ ________.
_____ _________ ____ _____ _______ ________.
_____ _____ _______ _______ __________ _____ __________.
_________ _____ _________ ____ ____.
__________ ______ ________ ________ ___ ____ ________ ________ __________ ________.
___ _________ ______ ________ _________ __________ _______ _____ ______ __________.
_____ ______ ___ ___ ___ ___ ____ _____ _______.
___ ________ ______ ___ ___ ___ _________ _______ ____ ___ ___ __________.
_____ _______ ______ ___ ______ ____ _____ _______.
_________ _____ __________ __________ _________ ___ _________ _________ _____ __________.
______ ______ ________ __________ ____ _________ ______ ____ __________ ___.
____ ____ _____ ____ ___ ____ __________ ________ _______ ____ ________ _________.
_____ ______ __________ __________ ____ __________ _________ ___ ___ ___.
___ _______ ________ ___ __________ __________ ____ ______ ______ _____ _____ ________.
____ _________ __________ ___ _____ __________ _________ _________ __________.
_______ ____ ______ _________ ___ _________ ___.
________ _________ __________ ______ ____ ____ __________ ___ ______ _____ ________.
________ ________ __________ ____ ______ _____ _______ __________ ____ __________ ________ ________.
______ ____ _________ _________ _________ ____.
_________ ____ _____ ___ ____ ___ _________.
_______ ____ _____ _______ _____ ________ ________ _______ ________ ________ ___.
__________ ______ ______ ___ __________ ___ __________.
________ ________ ____ _________ _________ ____ _____ ______ ____.
____ ____ _______ _______ ________ __________ ____ ________ ______.
_________ ___ __________ __________ ___ _________ ________ ________ ____.
______ _______ _________ _________ ________ _____ _____ _________ _________.
___ _________ _______ ___ ___ ______ _____ ________.
___ ___ _____ _______ ____ ___.
____ _______ ________ ______ __________ _________ _______ ________ ________ _______ _____.
_____ _____ __________ _________ _________.
__________ _______ ____ ___ ________ ___ _______ ________ ______ ___.
___ ___ _______ _____ _______ ___ ______ ___ _____ _______ ____ _____.
________ _______ ______ _________ ________ ______ ______ __________ ______ _____ _________ _____.
______ _____ __________ ______ _____ ________ __________ ____ _____ ______ _________ ____.
_____ ____ __________ ______ ________ ______ ________ ___.
Skip in 10
दी गई अवकल समीकरण है: [ (x^2y - 2xy^2)dx - (x^3 - 3x^2y)dy = 0 ] इसे इस रूप में लिखें: [ M(x,y)dx + N(x,y)dy = 0 ] जहाँ, [ M(x,y) = x^2y - 2xy^2, \quad N(x,y) = -(x^3 - 3x^2y) = -x^3 + 3x^2y ] अब देखें कि यह अवकल समीकरण सटीक (exact) है या नहीं। सटीकता की जाँच के लिए: [ \frac{\partial M}{\partial y} \stackrel{?}{=} \frac{\partial N}{\partial x} ] [ \frac{\partial M}{\partial y} = \frac{\partial}{\partial y}(x^2y - 2xy^2) = x^2 - 4xy ] [ \frac{\partial N}{\partial x} = \frac{\partial}{\partial x}(-x^3 + 3x^2y) = -3x^2 + 6xy ] चूँकि [ \frac{\partial M}{\partial y} \neq \frac{\partial N}{\partial x} ] इसलिए समीकरण सटीक नहीं है। अब इंटीग्रिंग फैक्टर ढूंढते हैं। यहाँ ( \frac{N_x - M_y}{M} ) देखें: [ N_x - M_y = (-3x^2 + 6xy) - (x^2 - 4xy) = -4x^2 + 10xy ] [ \frac{N_x - M_y}{M} = \frac{-4x^2 + 10xy}{x^2y - 2xy^2} = \frac{-4x + 10y}{x - 2y} \quad (\text{y से बाहर काटकर}) ] यह केवल (x) और (y) के सरल अनुपात में नहीं है, इसलिए मान लें कि इंटीग्रेटिंग फैक्टर ( \mu = \frac{1}{x} )। समीकरण को (\frac{1}{x}) से गुणा करें: [ \left( x y - 2 y^2 \right) dx + \left( -x^2 + 3xy \right) dy = 0 ] अब ( M = xy - 2y^2, \quad N = -x^2 + 3xy ) जाँच करें: [ M_y = x
_____ __________ ___ _____ ___ _____ ____ __________ _____ ______ _____ ___.__________ ________ _____ _____ _________ ____ ____ ______ _______ ___ _______ __________.
________ ________ _________ __________ ______ _______ _________ _________ ___.
_____ ____ ________ _____ ________.
_____ _________ ____ _____ _______ ________.
_____ _____ _______ _______ __________ _____ __________.
_________ _____ _________ ____ ____.
__________ ______ ________ ________ ___ ____ ________ ________ __________ ________.
___ _________ ______ ________ _________ __________ _______ _____ ______ __________.
_____ ______ ___ ___ ___ ___ ____ _____ _______.
___ ________ ______ ___ ___ ___ _________ _______ ____ ___ ___ __________.
_____ _______ ______ ___ ______ ____ _____ _______.
_________ _____ __________ __________ _________ ___ _________ _________ _____ __________.
______ ______ ________ __________ ____ _________ ______ ____ __________ ___.
____ ____ _____ ____ ___ ____ __________ ________ _______ ____ ________ _________.
_____ ______ __________ __________ ____ __________ _________ ___ ___ ___.
___ _______ ________ ___ __________ __________ ____ ______ ______ _____ _____ ________.
____ _________ __________ ___ _____ __________ _________ _________ __________.
_______ ____ ______ _________ ___ _________ ___.
________ _________ __________ ______ ____ ____ __________ ___ ______ _____ ________.
________ ________ __________ ____ ______ _____ _______ __________ ____ __________ ________ ________.
______ ____ _________ _________ _________ ____.
_________ ____ _____ ___ ____ ___ _________.
_______ ____ _____ _______ _____ ________ ________ _______ ________ ________ ___.
__________ ______ ______ ___ __________ ___ __________.
________ ________ ____ _________ _________ ____ _____ ______ ____.
____ ____ _______ _______ ________ __________ ____ ________ ______.
_________ ___ __________ __________ ___ _________ ________ ________ ____.
______ _______ _________ _________ ________ _____ _____ _________ _________.
___ _________ _______ ___ ___ ______ _____ ________.
___ ___ _____ _______ ____ ___.
____ _______ ________ ______ __________ _________ _______ ________ ________ _______ _____.
_____ _____ __________ _________ _________.
__________ _______ ____ ___ ________ ___ _______ ________ ______ ___.
___ ___ _______ _____ _______ ___ ______ ___ _____ _______ ____ _____.
________ _______ ______ _________ ________ ______ ______ __________ ______ _____ _________ _____.
______ _____ __________ ______ _____ ________ __________ ____ _____ ______ _________ ____.
_____ ____ __________ ______ ________ ______ ________ ___.
IGNOU ACADEMY
Your IGNOU journey, made easier.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
Continue Reading — It's Free
Sign in with Google to unlock more of this answer.
✓ Free access
✓ Unlock up to 60% of the answer
✓ No payment required
✓ Unlock up to 60% of the answer
✓ No payment required
Quick Google sign-in. No separate registration form.
Related Questions
The Pfaffian equation is integrable.
अवकल समीकरण को हल कीजिए। एक कण विरामावस्था से एक माध्यम, जिसमें प्रतिरोध
प्रति इकाई द्रव्यमान है, में नीचे गिरता है। v किसी भी समय t पर कण का वेग है। सिद्ध कीजिए कि कण द्वारा समय t में तय की गई दूरी
है, जहाँ g गुरुत्वीय त्वरण है।
Using Charpit's method, find the complete integral of the p.d.e.:
अवकल समीकरण :
$
को प्राचल विचरण विधि से हल कीजिए।
Find the integral surface of the p.d.e.:
through the circle .
Suppose that a thermometer having a reading of inside a house is placed outside where the air temperature is
. Two minutes later it is found that the thermometer reading is
. Find the temperature reading T(t) of the thermometer at any time t.
) हल कीजिए :