9. xy sin yz dV, where G is the rectangular box defined by the inequalities 0

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Q: 3 Evaluate x² 2 SOFT S S x² sin y dy dz dx

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Q: xcos^2(y)dx+tany dy=0.

A: Given : IVP x cos2y dx+tan y dy=0  ,  y1=0 We need to solve the IVP.

Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

Q: 1 If f(x,y) = tan-(x y) with x= cos(2 t),y= then sin(2 t) " df can be calculate as follwos: dt O1.…

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Q: 6.Solve the following boundary value probletn: at2 U(0, t) ='U(x, t) == 0 U(x,0} = sin x + 2sin 2x…

A: To Solve: The boundary Value Problem : ∂2U∂x2 = ∂2U∂t2U(0,t) = 0U(π,t)=0U(x,0)= sin x+2 sin…

Q: (e² + In y + ) dz + (; +Inz + sin u) dy =0 2ta Iny+y ln z-cos y C O e² - = C a Iny +y ln z+ sin y

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Q: Ex 21Eulers method dy-y= - y Xーツ ーメー

A: We have to use the Euler's Method to solve                           dydx=y'=x-yx+y, y0=1,…

Q: Find a solution to the initial value problem y' + sin(t)y = g(t), y(0) = 9, that is continuous on…

A: We have to solve this initial value problem:

Q: 1. What should be A for the path independent of (2,4) 2Ay – x dy y? XY + A dx+ (1,2) Moreover…

A: Consider the given integral

Q: d) s x sin sin (4x²) d x X Sin X-y=- / 7xーy=17 てる。4) Set Up only Area bounded between the lines…

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Q: 4. Evaluate: S. yx²dx + xzydy + xz?dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

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Q: 4ス+S fra) = 7 +2 Contromulily of he funihim ihe fumnim Discuss The at x= 1

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Q: 4. Find dy and Ay for y = 3/ – I+ 2x at r = 2 with da = Ar = 0.2.

A: Consider the following information: y=3x-1dx=∆x=0.2 Differentiate y with respect to x: dy=32x-1dx dy…

Q: If y=xtan(x) then dy at x = Tt is: dx

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Q: H.W.4 Find dy/dx for the following: 1) y= x+ sin x + sin 5x 2) y 32x + In (sin x) + In(sin 5x) 7) y…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 8. cos xsin y dx +(3xy+sin x cos y) dy C:boundary of the region lying between the graphs of y= and y…

A: Given:  ∫Ccosxsinydx+(3xy+sinxcosy)dy...................(i) where C is bounded by y=x4  and  y=x To…

Q: 12. Find the dicections at.which. the directronal.derivative af.f.(hg)..xSin xy.at.(,a).has.…

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Q: Solve the following boundary value problem Uz = a²uxx u(0, t) = 0, Uz (1, t) = 0 , u(x,0) = 5…

A: Result: Given heat equation is: Solution is given by: Where

Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

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Q: 4. Supposea function y = f(x) is so be revokved at x = e from point (a, b) to (c, d), what is the…

A: Please refer the attached image for complete solution.

Q: if x² + y² =t -- and x* + y* = t dy prove dx 1

A: Given, if  x2+y2=t-1t and  x4+y4=t2+1t2 To prove that  dydx=1x3y

Q: 2 4 Q3) Evaluate the integral || xe" dy dx 0 x?

A: LetI=∫02∫x24xey2dydxchange the orderI=∫04∫0yxey2dxdyLet∫0yxey2dx=x∫0yey2dx∫0yxey2dx=ey2[x22]0y…

Q: 3. Compute x' In x dx both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's…

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Q: 9. a) Apply fourth order Runge-Kutta method to dy 3x + y/2, y(0) = 1 dx to determine y(0.2) correct…

A: (a) The given differential equation is…

Q: True or False: For an IVP dy/dx = f(x,y); y(a)=b, if f(x,y) is not continuous near (a,b), then its…

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Q: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

A: A line integral is the integral of a function along a curve. The function can be scalar-valued or…

Q: . Solve the following boundary value problems. (a) y"+y =0 with y(0) = 0 and y (T) = 1. %3D %3D %3D

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 1. (x+ tan-ly)dx+() dy = 0 Boundary Condition 1. y 1, whenx = 0 %3D Al+y2,

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Q: #3. Suppose that h(x) is integrable and that ,h(x)dx=1 and S,h(t)dt = 6. Find a. Sh(x)dx b. –…

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Q: B. (y + e*seny)x + (x + e*cosy)dy = 0

A: The differential equation is given as  y+exsinydx+x+excosydy=0 Compare it with Mdx+Ndy=0 to obtain…

Q: 1 2 _2 If U= +¯ +y¯ +z¯ is not equal to 0 then prove x+y° + dU + du that dx = 0 dx dy

A: Given function is U=1x2+y2+z2. We have to prove  d2Udx2+d2Udy2+d2Udz2=0

Q: i need help to solve this: y''+ 5y' + 6y = δ(t-2) intial conditions: y(0)=0 ,  y'(0) = 1

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Q: 8. Find a continuous solution satisfying dy dr + 2xy = f(x) where = x if 0 < x < 1 0 if x ≥ 1 off…

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Q: .4 4-y Q3) Evaluate triple integral , S S dz dy dx.

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Q: 1 If y = tanu, u=v--, and v= lnx, dy at x=e? dx what is the value of Select one: a. 0 O b. 1 1 C. d.…

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Q: 3. Let u =x² – 2xy+2y' with x = s´ · Int and y = 2s ·t° . au au and at Find as

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Q: Find the general and particular solution that satisfy the boundary condition. (3x + y)dx – (x +…

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Q: For a. y′ =ln(y)+x,withy(1)=1. (Here x0 =1.) b. y′ =ln(1+y),withy(1)=0. (Here x0 =1.) Is it…

A: Solving for  a) y'=ln(y)+x            dydx=ln(y)+xdy=ln(y) dx+x dx Integrating:           ∫dy=∫ln(y)…

Q: y 1) x(In x – In y)dy – ydx = 0 Ans: = c (Xie, 2010) %3D 1+In y-In x

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Q: Problem 11 The volume of the solid obtained by rotating the region enclosed by  y=(x^2), y=6x,…

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Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

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

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Q: S, (x + 2y) dx + x dy. C consists of line segments from (0. 0) to (2. 1) and from (2, 1) to (3, 0)

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Q: Compute the general antiderivative S a"-1 cos(x")dx COS where n > 1 is an integer greater than 1.

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Q: 4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x…

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Q: 2 1 Evaluate the iterated integral S 18*y°dy dx. -2 0

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge - Kutta method, what is…

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