Which following ones are first order linear ordinary differantial equations? dy y +e* sin y de dy II =e sinx de d'y III dy +3y 0 4 de de A) Only I B) I and II C) Il and II D) only II E) only

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: Use Green's Theorem to evaluate the line integral. cx2 - y?) dx + 5y? dy C: x² + y² = 9 (x² .

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Q: Verify that u is a solution to the equation ugx + Uyy + u zz = 0. u(x, y, z) = e4z+3y cos(5z)

A: Follow the procedure given below.

Q: Let C be the line segment from [1 – i,2+ 2i). (a) Parametrize C. (b) Integrate 2 over C.

A: According to the given information, Let C be the line segments from [1-I,2+2i]. For part (b) it is…

Q: ди ди ду ду Find the cauchy-riemann equations of, f (z) = | z | sin z. əx' dy'dx' ðy,

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1. In…

Q: Let z = e* sin(y+a), show that %3D ôx? oy?

A: Given, z=e-xsiny+a, then we have to show that ∂2z∂x2+∂2z∂y2=0.

Q: Consider the order and linearity of the following equations: i. (y+t)dy/dt + y=1 ii. 3dy/dt + (…

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Q: Use Green's Theorem to evaluate (y? tan- a?) dx + (3.xy+ 4x – In(y² + 4)) dy, where C is the…

A: We need to evaluate integral.

Q: Verify Green's Theorem by evaluating both integrals y2 dx + x² dy = dA ду for the given path. C:…

A: In this question we can verify the Green's Theorem . i.e, ∫C M dx +Ndy = ∫∫R ∂N∂x-∂M∂ydA .

Q: Exercise 1 Use rectangular coordinates to evaluate [[[ y dV , where E is bounded by the planes x= 0,…

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Q: Use Green's Theorem to evaluate the line integral. (a) | e2a+y dx +e¬Y dy, where C'is the triangle…

A: In the question we have to evaluate integral. NOTE - As per Bartleby's policy we can not solve…

Q: 1. Verify that (t) = et, y(t) = e' satisfies the system %3D dx 3y3 dt dy y, dt %3D

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Q: Verify Green's Theorem by evaluating both integrals ƏM y2 dx + x2 dy = dA ду for the given path. C:…

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Q: Study the analytically of w = L_r(z) at the points z = 0, z = v2,z = -2i

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Q: divE = 0 divĦ = 0 curlĒ = %3| c Ət 1 DỂ curlĦ Using Maxwell's equations, show (V· V)Ē : c2 Ət?

A: Given:  ∇E=0∇H=0∇×E=-1c∂H∂t∇×H=1c∂E∂t

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: Solve the wave equation in two dimensions Utt = v²u u (x, y, 0) = sin 4y U (x, y, 0) = cos xcos3y…

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Q: 2. Let W be the union of the first and third quadrants in the xy- plane. That is, let W = xy 0 a. If…

A: According to our company gardening can answer only one question. If a specific questions are asked…

Q: Use Gauss's Law to find the charge contained in the solid hemisphere x2 + y2 + z² < a², z z 0, if…

A: Given:The Electric field, E→=xi⇀+yj⇀+7zk⇀Equation of solid hemisphere isx2+y2+z2≤a2       ,z≥0To…

Q: Find a solution to the Dirichlet boundary value problem for a disk. zu 1 du 1 Pu = 0, + -- ar? Osr<…

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Q: Show that the general solution to the two-dimensional Laplace's Equation. et = 0 is (Acosh(tx)…

A: We have to show that the general solution to the two-dimensional Laplace's Equation…

Q: Let C be the positively oriented square with vertices (0, 0), (2,0), (2, 2), (0, 2). Use Green's…

A: Let the given square be OABC which is positively oriented.

Q: Use Green's Theorem to evaluate the line integral S(x² + y²)dx + (x² – y²) dy where C is the…

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Q: Transform the equation (ry? - z) dz + (z²y + y) dy = 0 into the form of separable dit %3D O ( + 1)…

A: Question is solved.

Q: Wrons kiant y" + p(+) y # q (4) j'arlt)g =0 +q(4) j' +r (t)y=0 solotions of fifferential equations…

A: Determinant properties

Q: Find a piecewise smooth parametrization of the path C. 0 st<1 (ti+tj r(t) = %3D 1<t<2 (1, 1) y=x

A: Given rt=ti + tj                             0≤t≤1                                       1≤t≤2

Q: Suppose F = ∇ * A, where A = (y + sqrt(z))i + e^(xyz) j + cos(xz) k. Determine the flux of F outward…

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Q: (b) Apply the method of contour integration to prove that (2m de 2n Jo 2+cose 3

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Q: Find the Second appoximation for the System. X Sin y at (xo,,)= (1, 1). y=Cosx

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Q: Among all rectangular regions 0&lt;=x &lt;=a, 0&lt;=y&lt;=b, find the one for which the total…

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Q: Integrate f(x,y,z) = (x + y +z)/ (x² +y² +z? over the path r(t) =t i+tj+3t k, 0<a<t<b.

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Q: For a certain fluid flow field the velocity is given by V = [y² – x(1+ x)]i+ [y(2x + 1)]j+k. Show…

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Q: Use Green's Theorem to evaluate the line integra Icon (y − x)dx + (2x − y)dy - - for the given path.…

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Q: Solve Laplace's equation inside a rectangle 0srS L, 0SYS H, with the following boundary conditions:…

A: Consider the solution as ux,y=XxYy. Then, the Laplace equation becomes Yy∂2Xx∂x2+Xx∂2Yy∂y2=0. Divide…

Q: Evaluate the line integral Sa y dx +z dy, where C is the line segment from (4) (-1, 1, 2) to (2,3,…

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Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy for the given path. C: x =…

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Q: . The uejveciion of a beam is governed by the equation d'y + 81y = 0 (x) dx %3D where o(x) is given…

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Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x - y)dy for the given path. C: x =…

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Q: Consider Y; = 0 + 0,X¡ + E¿, i = 1,2,..,n, e, - N(0,0), the cov(ô,Y) = %3D

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Q: Use Green's Theorem to evaluate the line integral  ∫c (y-x) dx + (2x-y) dy for the given path. C:…

A: Given data-    The line integral -                          ∫c (y-x) dx + (2x-y) dy .    We have to…

Q: Use Green's Theorem to evaluate x' dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: Consider the 2nd order equation d²y + Sin dy + y? +y = 0. dt, Choose the right assertion A) the…

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Q: A fluid has density 600 kg/m3 and flows with velocity ū = ri + y. measured in meters, and the…

A: Here we have, Velocity v→=xi^+yj^+zk^ where x,y, and z are measured in meters.  the equation of…

Q: Verify Green's Theorem by evaluating both integrals aM | y? dx + x² dy = dA ax for the given path.…

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Q: Verify Green's Theorem by evaluating both integrals dx + x² dy = // | da ду дх for the given path.…

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Q: 2) fff (x² + y² + z²)ž dv D is the unit ball. Integrate using spherical coordinates.

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Q: Solve the BVP for the disk (exterior Dirchlet problem) v'u = 0, 1< r <o∞ u (1,0) = sin 0 + cos 20

A: The given function is ∇2u=0 The given condition is u(1,θ)=sinθ+cos 2θ We have to find the general…

Q: Solve the folleowing differntial equations by usina Lapace trans formation dy dt +243D 1 + 2 dt2…

A: Given Differential equation :

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.