Question
Solve:
Answer :
Word Count : 282
दिया गया अवकल समीकरण है $$ y' = \frac{z y^4 + x^4}{x y^3} $$ यहाँ $y' = \frac{dy}{dx}$ और $z$ एक नियतांक है। इसे इस प्रकार लिखा जा सकता है : $$ \frac{dy}{dx} = \frac{z y^4}{x y^3} + \frac{x^4}{x y^3} $$ $$ \frac{dy}{dx} = \frac{z y}{x} + \frac{x^3}{y^3} $$ अब यह समीकरण है : $$ \frac{dy}{dx} - \frac{z}{x}y = \frac{x^3}{y^3} $$ यह एक बर्नौली समीकरण है, क्योंकि इसमें रूप है ___ ________ _________ ____ _________ ____ ______ ________ _______.
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दिया गया अवकल समीकरण है $$ y' = \frac{z y^4 + x^4}{x y^3} $$ यहाँ $y' = \frac{dy}{dx}$ और $z$ एक नियतांक है। इसे इस प्रकार लिखा जा सकता है : $$ \frac{dy}{dx} = \frac{z y^4}{x y^3} + \frac{x^4}{x y^3} $$ $$ \frac{dy}{dx} = \frac{z y}{x} + \frac{x^3}{y^3} $$ अब यह समीकरण है : $$ \frac{dy}{dx} - \frac{z}{x}y = \frac{x^3}{y^3} $$ यह एक बर्नौली समीकरण है, क्योंकि इसमें रूप है ___ ________ _________ ____ _________ ____ ______ ________ _______.
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Related Questions
Find the general solution of the equation:
x(y²-z²)ux + y(z²-x²)uy +z(x²- y²)u₂ = 0
Verify that the differential equation:
z(x2-y2-z²)dx+(x+z)xzdy
+ x(z2-x2-xy)dz = 0
is integrable and find its integral.
State Euler’s theorem for homogeneous functions and verify it for the function:
अवकल समीकरण :
का हल प्राप्त कीजिए।
Show that for the function f given by:
यदि :
Z=x²y+2xy4
जहाँ x = sin zt
और y = cost
तो dz/dt ज्ञात कीजिए: (i) श्रृंखला नियम और (ii) प्रत्यक्ष प्रतिस्थापन से जहां t = 0 |
दिखाइए कि निम्नलिखित फलन f, (0,0) पर अवकलनीय है :
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