A ) find me heneral solutron and the Particular solutim S at isfying for the inidraI condition X" y'=Hy with Yro) =B and where N >l and A aud B are PeStive cunstants. Gener1 Sulutiun 2 y k) I Particular Sdutian i x CX)>

Q: 1. Given w = x²y³z+x*yz³, x = cos(4t),y = sin(5t),z = In(t). Write the tree diagram for . Then,…

A: NOTE: The equations provided in the bottom part of the question do not match with the equations you…

Q: A particle of mass m is moving in a one-dimensional region of space where there is a Coulomb-like…

A:

Q: (b) / = xyz dV if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

A:

Q: Determine the steady-state temperature distribution T(r, ) in a solid hemisphere of radius r b, in…

A: Given: Radius of sphere=R Volume density f(r)=Ar2e-2ra Total charge=Q To find: Temperature…

Q: Determine a region of the xy-plane for which the DE (y- x) y' = y+ xwill have a unique solution…

A: Consider a differential equation y'=F(x,y), y(x0)=y0. Then there exist a unique solution to this…

Q: 46.) (a) Parameterize S the 1st octant portion of the cylinder y² + z² = 9, 0 <x<4 (b) Use above to…

A: y2+z2  0≤x≤4x=uy=3 cos vz=3 sin vparameterise the surface ass(u,v)=(u   3 cos v   3 sin v)0≤u≤4,…

Q: (b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y…

A:

Q: And the Vorume of the solid gererated by rovolung the reglon boundid by the given ines't (urves…

A:

Q: 1. Under the paraboloid = 3z2 + y? and above the region bounded by y = x and r= y² – y

A: Find point of intersection of:  y=xx=y2-y y=y2-yy2-2y=0y=0,2

Q: Consider 6x (1+x²)² 2(x+y) (1+x²)² + 2y ý = Using the function V(x, y) = 12 + y² show that the…

A: What is Lyapunov Stability Theorem: Lyapunov stability theorem says that if a function is positive…

Q: 5. Evaluate Fale JJJ (²+ + ² dv, where a, b, c > 0, and & is the region given by E 22 + y² 2² 6² +2…

A: Given triple integral is ∫∫∫Ex2a2+y2b2+z2c22dVa,b,c&gt;0x2a2+y2b2+z2c2≤1 in the first octant. Now,…

Q: 9. let C G TR? be Simple Close d curve bounding the positively orierned a reyi'on D. IF Area cO)=|…

A: Given that, Area(D)=∫Cx2+2xy+2y+eydx+∫CAx+x2+xeydy

Q: Evaluate the triple integral∭E xy dV where E is the solid tetrahedon with vertices…

A: Given Data : Triple Integral ∬∫ExydV and E is the solid tetrahedron with vertices 0,0,0,…

Q: Hw.3 3 Find the areas for the following Vegions: Region boundded by y=x y , and Region bounded by…

A: To find the area of the following region :-

Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

A:

Q: 14.w.3 Find Ihe arcan region for he fllowwiy Regian honded.by.y= X- y=D and S= 2

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 12. Consider the lamina covering the regon x442-2,0EXET WH aunsity functionplx,u) = - 5x + 2u+5. 1ts…

A:

Q: Ive the following PDE with nonhomogeneous boundaries: PDE UttUxx = 0, BCs u(0, t) = sin(t), u(L, t)…

A:

Q: Since f(x, y) = 1 + y² and ðf/ðy = 2y are continuous everywhere, the region R in Theorem 1.2.1 can…

A: Given data: We are given that y=tan(x+c) is the family of the solution using initial value y(0)=0

Q: S/2,/2 e#" (ysin(z)dr + æsin(z)dy + cos(z)dz) J0,0, integrali altında tanımlanmış olan vektör alanın…

A:

Q: Integrate fcx)9,2) =X+y -Z over thep Poth from OLo.0.0) to A (2,1,2) given by, ostsi (C) = r z i…

A:

Q: 6. At time t, a particle moving in the xy – plane is at position (x(t), y(t)) where the x(t)and y(t)…

A:

Q: From the integoal equaiion coresponding to the following differentinl equations with given initial…

A:

Q: egral dS over the su 9, where n is th surface element

A:

Q: 1.13 Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

A: The given function is x4dx+xydy By green's theorem, the integral becomes, ∫06∫06∂M∂y-∂N∂xdxdy where…

Q: 2. Find the temperature distribution inside a solid parallelepiped with sides (a, b, c) whose faces…

A: Here, uxx + uyy +uzz = 0                                  .......1 with conditions, ux,y,z,0 = A…

Q: Problem 10 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=3x  about…

A:

Q: VBe. a telisinge change of enrables to evaluae. Hhe gren daule integral Riregron Ahelan bound bou…

A: According to the given information, it is required to use change of variables to evaluate the…

Q: Solve Laplace's equation, a2u azu = 0,0 < x < a, 0 < y < b, (see (1) in Section 12.5) for a…

A: We need to solve the Laplace equation with the following boundary values.…

Q: 1.Let 3 le the solid obtained by rotating by region shown in the fiqure about the Assume as3 and b=…

A: Given: y=ax(x-b)2 and y=0 and  0≤x≤b The rotation about the y-axis. Assume a=3 and b=1

Q: 3/5ketch, E Valuate & reverse the order of in tegration 2. ol X dy

A: We are looking at the following curves simultaneously: y = ex y = 1 x = 0 x = 2

Q: Consider the 1-D Burgers' equation in [-1,1] ди a?u дии + at The initial condition is: u(x, t = 0) =…

A: Solution is below

Q: Find the region bounderd ABOUE ly ther pauabola X= (y-2 and bounded kčlana by anothen panaivic Iy…

A:

Q: 5. the Following dovble iutegvoal evalua te with D 22-y dA where R is the Eraingular region ver…

A:

Q: 1. Use a change of variables to evaluate || ソーx dA where R is the trapezoid with vertices (1,0,…

A:

Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

A:

Q: 7. Prove that the SolutmM of y + y = o is B sinx (hint y= Xu) by using Bessel's Functron definstian…

A:

Q: (a) Calculate the centroid (7, y) of the region under the graph y = cos x for 0 < x <T/2.

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: Find the value of Res(f'(2), 20) if zo is an isolated singularity off.

A: Let us start finding the value of  Res(f'(z),z0)   z0 is an isolated singularity of f

Q: (b) Find the surface area of the portion of the paraboloid z-2-x -y above the xy- plane. AMINATION A…

A:

Q: Consider the region K = {x² + y² + 2² 0, y > 0, z < 0} Choose ALL OF THE FOLLOWING which are…

A:

Q: 3, Let R be the of: y: sinx region endlosed bu the grophs n enclosed by and 1 x70 . Groph R and…

A:

Q: Consider the functional S[y] = − y(2)² + √² ² + [² dx (31/1²) 2 with right-hand boundary condition…

A: As per the question we are given an objective functional S[y] and a constrained functional C[y]  And…

Q: Consider a potential problem in the half-space defined by z 0, with Dirichlet boundary conditions on…

A: The green function solution to the potential problem with this boundary for Dirichlet boundary…

Q: 1 9. Evaluate dV;where E is the solid between the spheres of radius 1 (x² + y² + z²)³/2 E and 2…

A:

Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

A:

Q: obtain the ualues of at x=0,1, o.2 using R.K method of fourth order Por the differential equalion…

A: (1) :- given differential Equation  y'=-y,  y(0) =1  We have to find value of y at 0.1 and 0.2  Take…

Q: 10. Find the minimum of the integral I[y] subject to the constraint TIy) = [, s° dx = 2 JL over all…

A: Consider the problem: Extremize I[y]=∫x1x2F(x, y, y') dx subject to J[y]=∫x1x2G(x, y, y') dx=L ,…

Q: 2. 7 3. Find the centroid of the region bounded by y 3, 3 to the nearest thousandth. nd Since you…

A: To find the centroid of the given region R by integration

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.