Let f(x, y) and g(x, y) be two homogeneous functions of degree m and n respectively, +y = 0, then show that f = ag, for some scalar %3D where m +0 and h = f +g. If (x- dy %3D a.

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Q: A necessary and sufficient condition that M(x,y)dx+N(x,y)dy=0 be a homogeneous equation is M and N…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x+ 8y + 12z on the elipse…

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Q: Prove that af +y. -yof=nf (x, y). əx (Hint: Differentiate both sides of the definition of a…

A: Given  a) x∂f∂x+y∂f∂y=nf(x,y)b) x2∂2f∂x2+2xy∂2f∂x∂y+y2∂2f∂y2=n(n-1)f(x,y)

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A: Solution:- μx=1x, y'+px y=qx, if y1=11x2+14x+13 Therefore, y'+px y=qx General Solution is yI.F=∫qx…

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Q: The function f (x,y) =e/*+3tan( y/x) is homogeneous of degree A) 3 B) 2 C) 1 D

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Q: Test the function def ined by f (x,y) = - x- 4y for its homogeneity. If it is homogeneous, give its…

A: Find your answer below

Q: Let z(x, y) be the function implicitly defined as the solution to TC -2x + y + z + sin(xyz) = %3D…

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Q: Find the weighted integration norm (f, f) = | f(x)f(x)w(x)dx of the given polynomial on C[0, 1].…

A: Norm of a vector is defined as f=f,f.

Q: f (x, y) = xlx - alny is %3D O homogeneous 0 degree O not homogeneous O homogeneous 2nd degree O…

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Q: What is the degree of the homogeneous funcrion f(x,y) = = tan A 0 B 3 C) 2 4x² - 2 [(x + 5)² ] -…

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Q: 3. Give an example of a homogeneous function of the form f(r.y, 2) of degree 3.

A: HOMOGENEOUS FUNCTION A function of the form fx,y,z is said to be homogeneous function of degree 'n'…

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Q: Show that if f(x, y) is homogeneous of degree n, then                                     xfx(x, y)…

A: It is given that fx,y is homogeneous of degree n,

Q: Let h (z) = fi v (2t) dt.Find h' (1). Show the computations that lead to %3D your answer.

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Q: Let E = {(x,y, z) | x² + y² < 1 and xy < z < 2} and let S be the boundary of E, oriented outward.…

A: Using Gauss divergence law:  ∯SF.dS=∫∫∫V∇·F.dV                   =∫∫∫V2+3-1.dxdydz…

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Q: Let f(x, y) = 6 - 3y³ - yx² + 2x² + 2y² and h(x, y) = 2x² + y². a) Find all the local maximum and…

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Q: (c) Determine the degree of the following homogeneous function (0/(x,y) = 4x² + 2y, (i) f(x, y) =…

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Q: Let f(x, y) = (2.8x – 2.7y) /3x + 0.5y. The formula of the differential df at M(2.2, 0.5) is | df =…

A: Given: Let, fx, y=2.8x-2.7y3x+0.5y To Find: To find the formula of the differential df at M2.2,…

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Q: linear or nonlinear.

A: A PDE is said to be linear if the dependent variable u and all its partial differential coefficients…

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Q: If y, (x) = e** is a solution of the D.E y" + p(x)y' + q(x)y = 0, where p(x) and q(x) are continuous…

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Q: Let z2=2+4i | [4 Im (2) +2 Re (2)] dz € = ž1=0 where C the parabola y = x² defined from z1 to z2 ·…

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Q: d.x = -2x + 5Y dt dy -2.x + 4y dt 5 cost X = \ sin t et 3 cost –

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Q: Determine the degree of the following homogeneous function (1) f (x, y) = 4x² + 2y*, (ii) f(x, y) =…

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Q: Let y1, y2,..., Yn be n linearly independent solutions of an nth order homogeneous ODE with constant…

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Q: Find the weighted integration norm (f, f) = | f(x)f(x)w(x)dx of the given polynomial on C[0, 1].…

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Q: 8. Consider the function of two variables f defined by 1 z = f(x, y) = 2x² + xy + 2². (a) Prove that…

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Q: The function f (x,y) =e" + 3tan an( y/x) is homogeneous of degree А) 3 в) 2 cC) 1 D) 0

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Q: Let f(x, y) = 6 - 3y³ - yx² + 2x² + 2y² and h(x, y) = 2x² + y². a) Find all the local maximum and…

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Q: A necessary and sufficient condition that M(x,y) dx+N(x,y)dy=0 be a homogeneous equation is А M and…

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