Solve the differential equation
where
The given differential equation is: \[ p^2 + 2p y \cot(x) - y^2 = 0 \] where \( ____ ____ _____ ____ _______ ___ ___ __________ ________.
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_______ _____ _____ ______ _______ _______ ______ ___ ______ _______.
________ ____ _____ ____ ________.
________ ___ _______ ________ _________ ___ ____.
________ _______ _____ _______ _______ ___ _____ ____ ____ _________.
_______ __________ ____.
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हल कीजिए :
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.
जैकोबी विधि से समीकरण
का पूर्ण समाकल ज्ञात कीजिए।
यदि ƒ और g स्वेच्छ फलन हों तो दिखाइए कि समीकरण
का हल होगा जहाँ,
Using the method of variation of parameters, solve the equation
हल कीजिए :
Find the general solution of the differential equation