Evaluate f (x + 2y)dx + (y – 2x)dy around the ellipse C defined by x = 4 cos 0, y = %3D | C 3 sin 0,0 < 0 < 2n if C is described in a counter clockwise direction.

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A: Given the boundary conditions is ∂u∂θr,0=0, ∂u∂θr,π3=0, u1,θ=sin2θ

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Q: 3 3 9 y x Figure 1: Paraboloid y = 9x² - 2² with y ≥ 0 2. Given F =. By using Gauss's theorem, find…

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Q: 1. Find the work done by F(x, y, z) = (-y,–x, z) on a particle that moves along the curve R(t) (2…

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" -…

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Q: Find the Jacobian of the transformation. x = 5e-2r sin(20), y= e²r cos(20) a(x, y) = alr, e)

A: Explanation of the solution is given below...

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Q: If we use the Laplace transformation, the solution y(t) of the following differential cquation: y' -…

A: Given y'-2y =1 and y(0) =2 Applying laplace on both sides       L(y')-L(2y) =L(1) We know that…

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Q: dx Solve the simultaneous equations dt dy - 2x + 2y = 1-2t, dt +x= 0. Given that dt *0, y= 0, dr =0…

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Q: Consider the following IVP: у" +у'%3D-сos x;B у(0) %3D а, у(0) -b Find the general solution. A y (x)…

A: Solution of the differential equation

Q: Find the Laplace transform of the equation: y′′+y′−3y=e-2t when y(0)=0, y′(0)=0

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Q: 7x Find the linearization L(x,y) of the function f(x,y) = e cos (5y) at the points (0,0) and

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Q: Use Laplace transformation to solve the initial value problem y' + 2y = u(t) sin (2t), y(0) = w,…

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A: We have to find an autonomous first order differential equation dydx=fy whose portrait is consistent…

Q: 1(t) and y2(t) be two funadamer y' + sin(t) y3D0, with initial con )=1 ,V,(0) = 0, 7 the wronskian…

A: Let y1 and y2 be two fundamental solutions for the DE:y''+y'+sintty=0, with initial…

Q: Find the Laplace transform, Y(s), of the solution of the IVP y" + 3y + 2y = cos(2t), y(0) = 0, y'(0)…

A: The given initial value problem is y''+3y'+2y=cos(2t), y(0)=0, y'(0)=1. Find the Laplace transform…

Q: 7. Evaluatexyddx+e*dy where C goes along the x-axis from (0,0) to (2,0) and then along the parabola…

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Q: Express a general solution to 2x (1 — х)у" + (3 — 10х)у — бу %3D 0 Using Gaussian hypergeometric…

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Q: Give the Laplace transform of the solution to y' + 3y-4 e* – 2 sin(2 x), y(0)=5]

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Q: Si se utiliza la transformada de Laplace resolver la ecuación diferencial X"+ 5X' + 6X = 3t – 3e-3t…

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Q: Show that the process X(t) = A cos At + B sin At (where A and B are RVs) is wide-sense stationary,…

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Q: -K Owhich methodisused to make U CHA) =\+C 픈 TIX Sin a Solution to the Problem initial and boundary…

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Q: Find the differential dy: y = In (sec2 (3* )). -2a+5 O tan (3-2+* ) dæ -2r+5 dy = (x – 1)…

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Q: Solve Laplace Equation in the circular domain 0 srs 1, with Dirichlet boundary condition, u(1,0) =…

A: Given, the Laplace equation                           urr+1rur+1r2uθθ=0             (1)in circular…

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Q: 10. Show that the function f(r, y, 2) =e+ cos 5z satisfies the Laplace equation

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Q: a When reduced to a linear DE of order one in z, the Bernoulli's equation dx becomes dz A + z( − 1)…

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Q: Consider the dynamical system dx sin(x) dt dy = e – 1 dt Around the fixed point at (0,0), integral…

A: Given:-               Consider the dynamical systemdxdt=sinxdydt=ey-1 Around the fixed point at…

Q: Exercise 1. Find the residues at z = 0 of the functions ez sinh(z²) 1 1 26 Z + z3 ' 25 and also find…

A: As per Bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: Assume x and y are functions of t. Evaluate dy for 4xy - 7x+4y3 = - 48, with the conditions dt dx =…

A: Explained below

Q: Example 10.26. Using Picard's method, find approximate values of y and z corre- sponding to x = 0.1,…

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Q: T'y" - 5xy = sin 3ry is a second order nonhomogeneous differential equatic Select one: O True O…

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Q: 1. -ay + A sin dy 2 = Br, dt

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Q: 1- f(-vt) ve x 1tve 117e x 1, wave which is mot a solilio to wave epuation. sinncost y at3 =…

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Q: Solve the initial value problem below using the method of Laplace transforms. y" +y' - 12y = -8 cos…

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Q: Solve the two-dimensional Laplace's equation J²u²u + dx² dy² 0 ≤ y ≤H, = cos I, subject to the…

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Q: Find the differential equation for the family of circles with center on the x-axis. A. yy" + (y') +…

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Q: DE 1. (1-x)y'-4xy +5y = cosx d'u du 2. at 3. d²u कर = d³x dx d²x +(4t-1)- +sin t - dt² dt dt3 4.…

A: To identify the type,order,degree, linearity if give differential equation.

Q: Q2:- a. b. Let u=x²-2xy + 2y³ with x = s²ln t and y = 2st³. Find au/as and au/at. find the total…

A: We need to solve the two questions.

Q: Use the Laplace transformation method to solve the IVP y" + y = e-2 sin t, y(0) = 0,y'(0) = 0

A: We need to find the solution of the given IVP by using Laplace transform4 The given IVP is

Q: 5.Express this model of an electric circuit d²y dy +6 +5y = sin10t, y(0)=0, y'(0)=1 dt² dt As a pair…

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Q: Which one of the following differential forms is exact? a. cos(x + y +z°)(2xdx-4y dy+2zdz) b.…

A: To find  Which one of the following differential forms is exact

Q: Use the Laplace transform to solve the initial value problem. y''+ 36y = sin(6t), y(0) = 1, y'(0) =…

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Q: Consider the undamped forcing problem d^2y/dt^2 + 4y = cos ωt. For what value of ω would resonance…

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