Q.4) Consider the problem 2x + Y dy dx 2x where R is the rectangular region enclosed by 2x + y = -2, 2x + y = –1,2x – y = 0, 2x – y = 2. (i) For thes problem finad a transformantin T from uv-plane to xy-plane. (ii) Find the Jacobian corresponding to T. (iii) Evalute the integral.

Q: -1 < x <0 The Fourier integral of f(x) = 1, 0<x<1 0, otherwise 00 (1 – cos(w)) sin(wx) dw lw 1. 00…

A: Given that fx=-1-1&lt;x&lt;010&lt;x&lt;10otherwise The Fourier integral of f(x) defined on -∞,∞ is…

Q: Consider the hyperbolic partial derivative equation Uzz = Uu – sin (x), rE [0, 1], t>0, with the…

A: Given,uxx=utt-sin x , x∈0,1, t&gt;0Boundary conditions: u(0,t)=ux(1,t)=0 , t&gt;0…

Q: , 0 0 u(0,1) — 0, и(п,г) %3D0 sinx, u (х,0) — 0 Utt = Uxx, u(х,0) 3D

A: Consider the solution: ux, t=XxTt and the conditions are X0=0=Xπ, T0=fx=sinx and T'(0)=0  uxxx,…

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y" - y'= et cos(t),…

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Q: Solve the integral ſ. (cx – y)dx + (ax + cy)dy along the curves x = y³ from (0,0) to (1,1) a – The…

A: Consider the integral I=∫ccx-ydx+ax+cydy along the curve x=y3 from 0,0 to 1,1. Given a=2 and c=8.…

Q: (1.-13) Show that the line integral (2xy+3)dx +(x² - 4z) dy-4 ydz is independent of path and (0.0,0)…

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Q: Q5. Find the Laplace Transform of the funetions x(t) and yıt), which satisfy the coupled first…

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Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

Q: 6. Let u (r, t) be the solution of the initial-boundary value problem ut = 9uzz 0 0, %3D uz (0, t)…

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Q: 4 +z² =1. 9 Evaluate xyz dV where E is the ellipsoid (in the first octant only) given by 3 E 4 Use…

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Q: Find the differential dy: y = In(sec² ( 3ª²–20+5 312-2x+5 O (E) None of the choices dy = 2 (x – 1)…

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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: 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: 17. Evaluate the line integral xe" dx +y sin yªdy along the triangular path consisting of the line…

A: Consider the given integral. I=∫Cxex2dx+ysiny2dy The given points are 0,0,2,3,1,0,0,0. Now, draw all…

Q: Suppose w = In(8x² + 2y² + 3z²), ¤= 9 cos(t) , y = 9 sin(t) , and z = 8Vt. Compute dw/dt in two…

A: The partial derivative of a multivariable function with respect to any of the variables can be…

Q: Problem 11 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=4x, about…

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Q: Suppose that z = xy² and x and y are differentiable func- tions of t with x =2,y = when t = -1. Then…

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Q: (1. 1. 1) Evaluate the integral (5xy + 22°) dx + 5xf dy + (12z + 1) dz. (0.0.0) (Hint. Try the path…

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Q: 2) Let 1 = f* cos y3 dydx. By reversing the order of integration of I, we get a. 1 = ²₂x cos y³ dx…

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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: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A: Given- s=x2+y2+z2 To find- dsdt in terms of dydtand dzdt, if x is constant. Concept Used- As the…

Q: Use the Laplace transform to solve the given initial-value problem. y''' + 2y'' − y' − 2y = sin(4t),…

A: Given: Given initial value problem is y'''+2y''-y'-2y=sin4t,y0=0,y'0=0,y''0=1

Q: 2. Using laplace transforms solve for x and y: dx dy + dt dt 2dx dy + + x +y = 3 dt dt subject to…

A: The solution is given as

Q: 15. Evaluate the line integral J. (3x²y* - 6xy ]dx + (4x²y³ - 3x°) dv, where C is any path from…

A: My=Nx means F is conservative vector field

Q: 1.6 Evaluate the line integral f x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

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Q: 3- Let µr1 = 2 in region 1, defined by 2x+3y-4z > 1, while µ2 = 5 in region 2 where %3D 2x+3y-4z <…

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Q: 6. Consider the problem u; + u²ux = 0, |x| 0 satisfying the initial condition u(x,0) = %3D 1+x2 a.…

A: The complete solutions are given below

Q: 1. The loop of y² = x * (4 - x) 2. у %3D 6х — х?, y = x² – 2x - 3. у %3D 2х y2 + 4x – 8 = 0 - 4. An…

A: Question 4 : Arch of y = (1/3)sin(x/3) First find out intersection points :  y = 0 (1/3)sin(x/3) = 0…

Q: Consider a semi-infinite elastic string that extends along the x-axis from x = 0 to infinity and let…

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Q: 15-5z Set up the iterated double integral SS dydr as dxdy such that: O i. from 0 to y/5, ii. from 1…

A: solution is given below

Q: 2. Use the Fourier transform to solve this transport equation for u = u(x, t), defined on the whole…

A: Given that                       2ut-3ux = 0 and  u (x,0) = e-x2            We can write this as…

Q: 15. Evaluate the line integral J. (3xy* - 6xy ]dx + (4x'y - 3x) dy, where C is any path from (1, 2)…

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

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Q: Use the Laplace transform to solve the system X +y -X = cost, x'+ 2y 0, x(0) = y(0) = 0. OA. x(t)…

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Q: Q.5 Use Fourier integral to solve the initial-boundary value problem Uzz + Uyy = 0, u(0, y) = 0,…

A: Given equation is  uxx+uyy=0                   (i) Let the solution of eq. (i) be ux,y=XxYy with…

Q: Consider the vectors x(¹) (t) = ( ) and x(²) (t) = ( 6 ). 6t (a) Compute the Wronskian of x(¹) and…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Problem 13  The volume of the solid obtained by rotating the region bounded by x=(y^2), x=5y  about…

A: Sketch the region using a graphing calculator The shaded region is rotating about the y=5 line

Q: Puestion 04: Use transform method to solve the following equation. Utt – Uxx = te¯*, 0 0 With the…

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Q: Using laplace transforms solve for x and y: dx dy + + 5x + 3y = e-t dt dt dx dy 2 + +x+y = 3 dt dt…

A: Laplace transform of (i) Ldxdt=sX(s)-x(0),  Ldydt=sY(s)-y(0)(ii) Le-t=1s+1

Q: 3. 1d Born approximation. For 1 dimensional scattering with potential V(x), it is also possible to…

A: Given: Gx,x' =12ikeikx-x' : x&gt;x'12ike-ikx-x' :x&lt;x'

Q: 1Byusing the Jacobian Jeber minant transform dx dy to drdo

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Q: 10) Consider the initial value problem y" + y = d(t – 27), y(0) = 0, y'(0) = 1. %3D %3D Using…

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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: O Evaluate the path integral between the points A = (1,3) and B = (2,5) of: (x²y + 2y)dy, with y =…

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Q: a) Sojlve the initial vajlue problem using Laplace transform UTM y + 2y = 26 sin 3t, y(0) = 3. UTM…

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Q: Exer 1. Solve the following first-order boundary value problem 2 u +4 u, + 40 u = u(z, 0) = e* 60…

A: We have to find solution of given pde

Q: 1-6 Use an appropriate form of the chain rule to find dz/dt. 1. z = 3x²y*; x = r^, y = r² 2. z =…

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Q: 5. Let f(x,y)=2y² +3z² - 4p +6. Find the absolute maximum and minimum values of f on the region z²+…

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Q: 1. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)], what special case is…

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Q: 2. By Laplace transform solve the boundary value problem 00 %3D u(0, t) =0, u(1,1)= 0, 1 >0 Subject…

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