सत्यापित कीजिए कि समीकरण
समाकलनीय है और इसका पूर्वग ज्ञात कीजिए।
यह समीकरण \( 2(y+z)dx - (x+z)dy + (2y - x + z)dz = 0 \) एक विभक्तीय समीकरण है। हमें यह सत्यापित करना है कि यह समाकलनीय है और इसका पूर्वग ज्ञात करना है। ________ ____ ___ _________ _______ ______ ____ _________ _____.
__________ _________ ______ ______ ________ ________ ________ ________ _________ ___ ________.
__________ __________ _____ _______ _____.
___ __________ _____ ___ ________.
____ ____ ________ _________ _______ ____ ______ _______ ___ ____.
_________ ____ _____ ________ _______ _________ __________ _________ _________ ___ _____.
___ _________ __________ _____ _______ _________ _________ ______ __________ ___ __________ _________.
_________ _________ ________ ______ _________.
___ __________ ________ _______ __________ _____ ___ __________ _____.
____ ____ ______ ___ _________ _____ _____.
___ __________ _______ ___ _________.
___ ____ ___ ___ ____ __________ ________ __________ ______ _________ __________.
___ ____ __________ _____ __________ _______ _________ _______ _______ ________ ___ __________.
_______ _______ _________ __________ ___ _________ ________ ____.
_________ _____ _________ __________ _______ ___ ______.
_________ ________ ______ ___ _________ ____ _______ ___ _______ _____ ________.
Get Full Answer on WhatsApp
Find the differential equation of the family of surfaces What is the order of this p.d.e?
Classify the following statements as true or false. Give a short proof of a counter example in support of your answer.
i) The solution of the differential equation exists, but is not unique.
ii) The differential equation representing all tangents ty = x + t2 at the point (t², 2t) to the parabola y² = 4x is x(y')² + yy'+1=0
iii) The p.d.e. auxx + 2b uxy + cu,yy = 0 where a, are constants is irreducible when b2 ac = 0
iv) The functions f1(x) = cos²x, f2(x) = sin²x, f3(x) = sec² x and f4(x) = tan²x are linearly dependent on the interval ] - π/2, π/2 [
v) The solution of the second order partial differential equation involves two arbitrary constants.
Using Jacobi’s method find the complete integral of the equation
यदि ƒ और g स्वेच्छ फलन हों तो दिखाइए कि समीकरण
का हल होगा जहाँ,
A mass m , free to move along a line is attracted towards a given point on the line with a force proportional to its distance from the given point. If the mass starts from rest at a distance x0 from the given point, show that the mass moves in a simple harmonic motion.
Solve the PDE
If ƒ and g are arbitrary functions of their respective arguments, show that is a solution of
where,