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

Q: Let I = L,x? cos(x + 1) dx. The approximation of I using the two-point Gaussian quadrature %3D…

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Q: 2: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G(x, y) = x³y² + y² sin…

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Q: ZX = 24, XY = 10, and YZ = 26. Find cos Y. %3D

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Q: 3. Solve the Laplace equation inside a 60° wedge of radius 1 subjected to the boundary conditions du…

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

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: az az Use the chain rule to find and as at z = In(4x + 3y), x = s sin(t), y = t cos(s) az as az %3D…

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Q: differenetiate parametrically to find dy/dx in terms of t:  x=1/t+1 , y=2t^2-4

A: please use according to form i did solved two equation because your question is not write clear that…

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...

Q: 4x Find the linearization L(x,y) of the function f(x,y) = e cos (3y) at the points (0,0) and0,

A: Answer is given below

Q: Suppose an undamped forced spring mass system is driven by the equation + 9x = f(t), dt where the…

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Q: dx/dt + 4x = cos(2t), x(0) = -1 Find x(t)

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Q: dw Use the Chain Rule to find where w = cos 8x sin 2y, x = and y = t*. dt 4' dw II

A: w=cos8x sin2y  , x=t4 and y=t4 dxdt=dt4dt=14 dydt=dt4dt=4t3   ∂w∂x=8 cos8x cos2y ∂w∂y=sin8x -2 sin2y…

Q: 3.) Calculate the curve integral f (1 – a² + y²) dx + (1 + x² – y°) dy. Here C consists of the…

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Q: y = In(sec t), x = log(cosec t) In(sect), x %3D %3D

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Q: dw Use the Chain Rule to find where w = cos 12x sin 4y, x = - dt and y = t". 4 dw

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Q: Let w(x, y, z) = x² + y² + z² where x = sin(7t), y = cos(-3t), z = e-4t. dx dy dz dw dt dt' dt dt…

A: Given problem:- wx,y,z=x2+y2+z2,x=sin7t,y=cos-3t,z=e-4t Find dwdt

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

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Q: Draw the bifurcation diagram for dy/dt = y(a-y)

A: We can use concept of critical points in order to solve the given problem.

Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

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Q: Compute dy/dx and d^2y/dx^2 for the following parametric functions

A: Given: y=e2tsin2tx=e2tcos2t

Q: x+ y dydx = Inß ху %3D Find B.

A: The objective is to find the value of beta.

Q: Calculate the “n” of the DE with the given 6y^2dx-x(2x^3+y)dy=0

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Q: find the linearization at x = a: y = ex ln x, a = 1

A: fx=ex lnx,  a=1 Differentiating with respect to x, we get f'x=dexdx·lnx+dlnxdx·ex=ex lnx+1xex Now,…

Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

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Q: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

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Q: Q5. Evaluate the triple integral cos(y²) dz dx dy.

A: The given triple integral is;  Cos(y2), z from 1 to 3, x from 0 to y, y from 0 to sqrt(pi/2).

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…

Q: Let -2+ sin(t) i = 1(0) = x0- I, 2 + cos(t) Vhat is r(t)? Is this system asymptotically stable,…

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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: -2-x Q1) Evaluate the integral S* dy dx using polar coordinate 0,

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Q: Q5. Evaluate the triple integral ²³ cos (y²) dz dx dy.

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Q: Find the potential P(x,y) attached to the exact ODE 2x sin(y) +x² cos(y) y' = 0

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Q: Find the residues of the following functions at each of its singularities. (i) sin(rz) (ii)…

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Q: (b) Use a graphing utility to find dx/dt, dy/dt, and dy/dx at the parameter t 6. dt TO -/-

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Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *() + 1. 2tan -1 2tan-1 + C ()…

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Q: Let z = x*y + 3xy* where x = sin 2t and y dz find = cos t. Use the chain rule to %3D when t = 0. dt

A: z=x2y+3xy4where x = sin 2t and y = cos t We need to find dzdt when t =0 Let's use the chain rule :…

Q: 10. Show that the function f(x, y, z) = e³x+4y cos 5z satisfies the Laplace equation.

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Q: dz Use the Chain Rule to find : z = = cos(x + 4y),x = 5t*, y = - %3D dt

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Q: Compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dy. C is a unit circle with counterclockwise…

A: We need to compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dywhere c is a unit circle Equation of…

Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

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: solve the first order differential using Lapace transformation dy + y = sin(t), with y(0) = 1 %3D dt

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Q: E). f(x, y) = sen?(r2 – 0²) + In(r0 + 0), r = Vx2 + y² 0 = arctan con -

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Q: roțațion 90° counterclockwise about the origin Ay R T

A: The figure SRT is to be rotated counter-clockwise about origin by 90°. The resulting figure will be…

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

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Q: Let (x² – x)ʻy" +y' -y=0,the D.E has regular singular point at x =

A: The DE x2-x2y''+y'-y=0. Then we have to find the regular singular points for the given DE.

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.