Question
State Euler’s theorem for homogeneous functions and verify it for the function:
Answer :
Word Count : 327
Euler's Theorem for homogeneous functions states that if \( f(x, y) \) is a homogeneous function of degree \( n \), then: \[ x \frac{\partial f}{\partial x} + y \frac{\partial f}{\partial y} = n f(x, y) \] Now, let's verify this theorem for the function \( u = \frac{x^3 + y^3}{x + y} \). ### Step 1: Find the partial derivatives of \( u \). The function is \( u = \frac{x^3 + y^3}{x + y} \). #### Partial derivative with ________ _____ ______ __________ ________ ______ ______ ____ ________ _____ ______ ___.
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Euler's Theorem for homogeneous functions states that if \( f(x, y) \) is a homogeneous function of degree \( n \), then: \[ x \frac{\partial f}{\partial x} + y \frac{\partial f}{\partial y} = n f(x, y) \] Now, let's verify this theorem for the function \( u = \frac{x^3 + y^3}{x + y} \). ### Step 1: Find the partial derivatives of \( u \). The function is \( u = \frac{x^3 + y^3}{x + y} \). #### Partial derivative with ________ _____ ______ __________ ________ ______ ______ ____ ________ _____ ______ ___.
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Related Questions
Find the complete solution of the equation px + qy = pq.
Find partial derivatives fx and fy for the function:
f(x,y) = 5x4y2 + 6x2 y3
at the point ,(1,-1)
हल कीजिए :
y'=zy$+x 4 / xy3
द्वारा दिए गए फलन के लिए दिखाइए कि :
लेकिन 
का अस्तित्व नहीं होता।
द्वारा दिए गए फलन के लिए दिखाइए कि :
लेकिन का अस्तित्व नहीं होता।
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.
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