(C) Evaluate the integral (2x-y dx+(x +3y kdy along the given paths= (i) C: ū = (1+2)i+(4 -r) (ii) C: line segment from (0,1) to (2,7). from (0,0) to (3,3) %3D

Q: 2. Solve the general solution for the First Order Linear DE. удх %3D (еУ + 2ху — 2х)dy

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Q: 3 3 4 Evaluate the integral S [(?+y?+?)dz dy dx. 0 0 0 3 3 4 S[?÷+²)dz dy dx=O 0 0 0 (Type a…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: (a) By using thẻ chain rülé and the dérivative (1, (1xl) = {"1, if x>0 if x<0' d %3D dx 1-1, find -…

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Q: Determine the Integrating factor of the DE: y (2³e™y – 3) dæ + x (y+ x*e®v) dy = 0 -3 1

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Q: DE 1. (-x)y-4xy +5y = cosx 2. d²u d'u 2x² at³ 3. d³x 12 des -2 d²x +(4t-1). + sin t dt² 4. √1+ (v)³…

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Q: (2) Let F(x, y) = (cos(y)+2x, -x sin y+1). Show that F is path independent by finding %3D a…

A: For the given vector function to be independent, it must be derived from a potential scalar function…

Q: Find an integrating factor for the DE y(4x – 3y – 3)dx +x(x– 2y –- 1) dy=0

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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: 3.4.4 Sketch the domain of integration and evaluate 2x 1-x dy (a) dx (b) Laxf d.x 2 Xx² + y²² dx dy…

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Q: The solution of (1+y²) + (t- elan-ly Y =0 is: -1n dy %3D dt Select one: a. 1 t 3D elan-ly e2tan-ly O…

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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: 2-x Consider the integral [ff av = √₁² √²-²² √²-* [[ [* dV 0 0 S (a) Sketch the solid S. dz dy dx.

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Q: Evalúe la integral iterada. S S xe" dædy 2e-1 3 4 бе-1

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Q: (b) Solve the integral [(3x – y)dx +(2x +3y)dy along the curve x = y' from (0,0) to (1, 1).

A: Solution of question as follows

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: cos(x + y)dx + (3y ^ 2 + 2y + cos(x + y))dy = 0, with the boundary condition of y(1) = -2.

A: We have to solve the initial value problem cos(x+y)dx+(3y2+2y+cos(x+y))dy=0 with the boundary…

Q: Express the solution of the given initial value problem in terms of a convolution integral y" + 12y'…

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Q: Reduce the linear DE (2xy+x² +x*)dx-(1+x)dy=0 to dy standard form + yP(x) = Q(x). dx dy…

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Q: Express the solution of the given initial value problem in terms of convolutional integral. A. y" +y…

A: Given differential equation is y''+y'+54y=1-u(t-π);         We have to express the solution of the…

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: 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: Find an integrating factor for the DE y(4x – 3y – 3) dx +x(x- 2y – 1) dy=0_

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Q: y3 (b) Solve the integral . (cx – y)dx + (2x + y)dy along the curves x = from (0,0) to (1,1)

A: The given problem is to evaluate the given contour path integral over given path x=y3.

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: The Integrating Fachor for the DE y dx- Ge-2x)Jdy -2y None of These

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Q: The second order homogeneous Cauchy-Euler equation defined by: 2d²y +bx- dy ォマ +cy=0 dx2 dx (ay"…

A: We have to choose the correct answer

Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

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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: 3D In Vi dt y = x/2

A: First of all we will evaluate  ∫lntdt=∫ln(t)12dt=12∫ln(t)dt=12ln(t)∫dt-∫ddx(ln(t))∫1dtdt(used…

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: 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: The total differential of the function: z=x*e3y . .A dz = 3x "e3Y dx +4x³e3Ydy. .B dz= 3x"dx +e3ydy.…

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Q: c) Use dU = 8Q-PdV to compute the heat, QD¬A, associated to the process D→ A along the black…

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Q: Let f(x, y,z) = x² sin y + y e², where x = t + 3,y = net-1 and z = ln 2t. %3D df at t = 1 is: dt…

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Q: cos(x + y) dx +(3y² + 2y + cos(x + y))dy = 0, with the boundary condition of y(1) = -2.

A: Here given differential equation as cosx+ydx+3y2+2y+cosx+ydy=0This equation is of the form…

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y)=3x<y becomes dx dz 1 A…

A: Topic  =Differential equation Correct option  = A

Q: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

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Q: Find the differential of the function y = In(S - 2x) 2dx dy = (5-2x) dy = (5 – 2x )dx -2 (5-2x)dx…

A: Given : The function y = ln(s - 2x).   To find the differential of the function y = ln(s - 2x).

Q: 1. Determine the general solution of (x 3y )dx – x dy = U

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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: 1-8 Evaluate the iterated integral. LLL 1. (x2 + y? + z?) dx dy dz 0, 1/2 2. 1/3 | zx sin xy dz dy…

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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: dy When reduced to a linear DE of order one in z, the Bernoulli's equation +yl-)= 3x3y² becomes dx…

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Q: B. Integration by Parts 1. xcosx dx

A: We know that integration by part formula is given as  ∫uv dx = u∫vdx - ∫dudx∫vdxdx To evaluate: ∫x…

Q: 1 Find skewness and kurtosis for the RV X with PDF f(x) = 2T -∞ < x < x.

A: PDF of X,  fX(x) = 12πe-x22, -∞&lt;x&lt;∞ So, μ = E(X) = ∫-∞∞x f(x) dx=∫-∞∞x 12πe-x22 dx=0 [as…

Q: Evaluate xsec¬xdx using integration by parts. OA x2 -sec-1x-(x² – 1)3/2+c 2 O B. x? 1/2 2 Oc x2…

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Q: What is the integrating factor of 6y²dx – x (2a + y) dy Oy-2 Oy? Oy

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Q: the separable Pential equation dy In(x³) dx ху subject to the initial condition У(1) %3D —3.…

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Q: (b) Solve the integral (3x– y)dx+(2x+3y)dy along the curve x = y' from (0,0) to (1, 1).

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