The following PDE u + u = 0 O a. Homogeneous (on the x-y plane) Ob. Nonhomogeneous on the x-y plane, but it is homogeneous on the first quadrant. OC. Nonhomogeneous (on the x-y plane) od. Cannot be said to be homogeneous or not, because it is not a linear PDE

Q: 7) z dV, E is the solid enclosed by the cylinder r2 +y = 1, and the E planes z = 0 and z 3.

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Q: Which among the following DE is/are homogeneous? * 2 punt i (X +2y)dk +(ax+y) dy =0 i dxyy = ytHl x…

A: We will find out the required solution .

Q: 1) Find the volume of the prism whose base is the triangle in the xy-plane bounded by the x-axis and…

A: To find the volume of the prism described we just need to evaluate the given double integral…

Q: The differ en tial equation yʻz + 2y'e* = 0 is (a) linear (b) separable (c) homogeneous (d) exact

A: The given differential equation is: y4x+2y'ex=0

Q: Transform rydy = y²dx + ydy into a separation variable form. dr ydy = 0 %3D O de dy : = 0 x-1 fip O…

A: Solving the problem by the said method.

Q: wnich of the followi ng functrons is homogeneous? 5x - 12メy ty? Po.) sm xy Ci) eln xy 2

A: To find which of the following function is a homogeneous function. A)fx, y=5x3-12xy+y3B)fx,…

Q: Consider the PDE y Ur + a Uyy + Uz – Uy = r² + y? In what region of the xy-plane is this PDE…

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Q: If f (0)=f'(2), find the difference c-2d for the following cubic spline S(x) with clamped boundary…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 4+ x² + y?, the cylinder E x2 + y? = 1, and…

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Q: The surface of many airfoils can be described with an equation of the form xa₁x y ‚ = + 0 = ₂2 [²₁…

A: You can find matlab code and answer for this problem in next step

Q: Let Ly)= x²y"- x(x+2)4'+ (X+2)y as Consider the homogeneous diffeuntial equation, Lly)=0 (*) is show…

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Q: Determine whether the DE hass homogeneous coefficients. If it has, find the implicit solt (x2+2ху -…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 2 + x² + y°, the cylinder z² + y² = 2, and…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 5+x +y, the cylinder a2 + y = 1, and the xy…

A: The objective is to evaluate ∫∫∫EezdV, where E is enclosed by the paraboloid z=5+x2+y2, the cylinder…

Q: Without using the formula (Gauss), calculate S=∂E∫F(x).n(x)ds, where F(x) = x32k ,E : x12 + x22≤ x3,…

A: Typing the equation may be some mistake. 0≤x3≤1 and another 0≤x3≤11, first one i accept.

Q: If f′(0)=f′(2), find the difference c-2d for the following cubic spline S(x) with clamped boundary…

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Q: tind the value of the consrant (min) that makes the D-E j X dx -CyfmX) dy so (Homogeneous, exact,…

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Q: If b = 6 cm, c = 3 cm, h = 6 cm, and a = 2 cm, the centroid of the area about x axis is equal to:…

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Q: Show that the value of ∮C xy2 dx + (x2y + 2x) dy around any square depends only on the area of the…

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Q: 2. Consider the DE y(4) – 4t²y" + 4y" = 0. (a) Is the DE linear? (b) Is the DE homogeneous? Why? (c)…

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Q: Consider the PDE Y Urr + x Uyy + Ux – Uy x² + y? In what region of the xy- plane is this PDE…

A: compare the given equation with Auxx+Buxy+Cuyy+Dux+Euy+Fu=G A=y,B=0,C=x,D=1,E=-1 calculate B2-4AC…

Q: Find the difference c-d for the following cubic spline S(x) with natural boundary conditions: S(2) =…

A: To find - Find the difference c - d for the following cubic spline S(x) with natural boundary…

Q: Evaluate fff (3x + 2y)dV, where S is the solid bounded above by the plane z=4, below by plane z=0…

A: ∫∫∫(3x + 2y) dV=∫∫∫(3x + 2y) dxdydz = ∫z = 04∫y = -13∫x =-11(3x + 2y) dxdydz = ∫z = 04∫y = -134y…

Q: please explain it step by step

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Q: 5. Evaluate Sl. x2 dV where is the solid that lies within the cylinder x² + y² = 4 above the plane z…

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Q: By making an appropriate change of variables, evaluate the double integral = || (x + y)e²-y° dædy R…

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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 ] -…

A: We have to find out degree

Q: Find the difference c-2d for the following cubic spline S(x) with natural boundary conditions: =…

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Q: 1. Use the cylindrical coordinate to evaluate ff. x² + y²dV _where G is the solid bounded by…

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Q: Consider the PDE y u + Uyy + u, - Uy = 2 +y? In what region of the xy-plane is this PDE elliptic? xy…

A: The objective is to find in what region of the xy-plane the pde is elliptic.

Q: 7.* Give the candidates to local extrema (maximum or minimum) of f(r, y, z) = 2z – y – r under the…

A: The solution to the given question is as follows.

Q: The following PDE u + u; = 0 а. Nonhomogeneous (on the x-y plane) b. Nonhomogeneous on the x-y…

A: Since, the term on right hand side is zero or without derivative term is zero.

Q: Evaluate ||| Vx2 + y2 dV, where E is the region that lies inside the cylinder x2 + y? = 25 and…

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Q: Evaluate || F.ndS F = xi + yj+(z² –1)k if and o is the curved surface of the cylinder y = \4-x? from…

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Q: The linear DE.s is called homogeneous if * R(x) is equal zero True O False O

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Q: 15. Evaluate SLL:(z+1)dV where E is the solid enclosed by the paraboloid y = x2 + z² and the plane y…

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Q: 11. Let D be the solid inside the cone z = √²+ y², inside the sphere x² + y² +2²=9 and above the…

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Q: Given that the total flux across the surface, S of the tetrahedron bounded by the planes x= 0, y=0,…

A: Given Vector field is F = 2xi + 3yj - zk

Q: Evaluate e dV where E is enclosed by the paraboloid z = 6 + x² + y°, the cylinder 2? + y? = 5, and…

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Q: YouTrylt 3 Evaluate the following triple integral S0 x dV, where E is bounded by the paraboloid x =…

A: The triple integrals involve the integration with respect to three variables, x,y and z. Similar to…

Q: The linear DE.s is called homogeneous if R(x) is equal zero True O False O

A: True

Q: Evaluate e dV where E is enclosed by the paraboloid z = 4+x² + y°, the cylinder x² + y? = 3, and the…

A: Here we have to evaluate ∫∫∫E ez dV , where E is the enclosed by the paraboloid z=4+x2+y2 , the…

Q: 1. Evaluate ſſ, y dS where S is the portion of the cylinder 4x² + 2y² = 16 %3D that lies between z =…

A: Given S is portion of cylinder 4x2+2y2=16 that lies between z=0 and z=7. Parametrize the surface s.…

Q: 1) In rectangle JKLM, JN = x + 3 and JL = 3x + 1, select all that apply. %3D %D K N M A) NL = 4 B)…

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Q: The measurements x1 = 10m, x2 = 8m, and x3 = 6m represent the sides of a rectangular parallelepiped…

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Q: By making an appropriate change of variables, evaluate the double integral (x + y)e²"-v° drdy where…

A: Suppose that we want to integrate f(x,y) over the region R. Under the transformation the region…

Q: 5. Use Cartesian coordinates to evaluate Jff ² av D where D is the tetrahedron in the first octant…

A: Given 2x+3y+z=6

Q: By making an appropriate change of variables, evaluate the double integral I = (x + y)e²²-y², dædy…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x? + y?, the cylinder x? + y? 5, and the…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.