जैकोबी विधि से समीकरण
का पूर्ण समाकल ज्ञात कीजिए।
जैकोबी विधि (Jacobi's Method) का उपयोग करके दिए गए समीकरण का पूर्ण समाकल (complete integral) ज्ञात करने के लिए, हमें निम्नलिखित चरणों का पालन करना होगा: ### दिया गया समीकरण: \[ 2u_1 xz + 3u_2 y^2 + u_2^2 u_3 = 0 \] ### चरण 1: समीकरण को जैकोबी के रूप में लिखें जैकोबी विधि के अनुसार, समीकरण को निम्नलिखित ____ _____ ________ ______ ___ __________ _____ _______ ___ ________.
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Solve the following differential equations:
i)
ii)
iii)
प्राचल विचरण विधि से समीकरण हल कीजिए। को
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.
Find the general solution of the differential equation
जैकोबी विधि से समीकरण
का पूर्ण समाकल ज्ञात कीजिए।
अवकल समीकरण y² ln y = x py + p² का व्यापक हल ज्ञात कीजिए। क्या समीकरण का कोई विचित्र हल है?
Solve the PDE