Use Green's Theorem to evaluate Se (yæ² – 3) dx + (x³ + 4) dy where Cis shown below. y (-3,3) •(6.3) -3 -2 -1 1 4 5 6. en 2.

Q: 5. Use Green's theorem to evaluate where C is shown below (6y - 9x) dy — (xy - x³)dx (-1,4) (-1,-1)…

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Q: if y= e-e-X dy %3D Show that %3D e* te*

A: We have to prove this equation

Q: 2) (1+ e*/y)dx + e*/y (1 – 2) dy = 0 Ans: x + ye*ly = c (Bali, 2007) %3D

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Q: Find af af and f(x, y) = etry In(6y) af 4yln(6y)e^(4xy) af 1/ye^(4xy)+4xIn(6y)e^4xy dy f(x, y) = cos…

A: In the first part the answer is correct but you have mistakenly not taken bracket for 1/y . You can…

Q: Answer the following questions for the DE. (y – 2)dx + (3x - y)dy 0 %3D What type of DE is shown?

A: (y-2)dx+(3x-y)dy=0  is first order non  linear ordinary  differential equation

Q: If u = x? + y? + z?, where x = e2t, y = e2t cos (3t), z = e2t sin (3t), %3D du at t= 0 is dt then

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Q: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

A: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

Q: and y = - V 8) Let ze, where x = √uv and Find dz dy in terms of u and v.

A: Given: z=ex2y x=uv y=1v To find dzdv in terms of u and v

Q: az əz 1. ax' dy If z = In(e* + e"), show that %3D %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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

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Q: 1. DETAILS LARAPCALC9 5.2.004. Identify u and du/dx for the integral fu"(du/dx) dx. / 4x3 Vx4 + 1 dx…

A: we have to identify u and du/dx for the integral ∫undudxdx Given integral , ∫4x3x4+1

Q: If z= t(x,y), where X = rCOse and y= rsine, %3D Show that 12 dz 12 dz dz dr dz del + dx

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Q: 1. If y = V6x + 1, then what is Y? dy? %3D dx dy a. 2(6x – 1) 3(6x + 1)7 2(6x + 1) dy С. dx %3D %3D…

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Q: tan(): '(), Suppose z = x = u cos(5v) , and y = u sin(5v) . Compute dz/du and az/dv in two different…

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Q: 3. Use Green's Theorem to evaluate J(* -6y)dx+(y +10y)dy where C is shown below.

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Q: - Evaluate the follwoing | r" exp(ax")dx where a + 0 and m+l = 1, 2, 3, ...

A: Given integral is, ∫xmeaxndx Substitute, u=am+1nxm+1dudx=m+1am+1nxm+1dx=1m+1am+1nxm+1du Then,…

Q: The DE: dY - 4xy +5y² xy + 3x? can be transformed into a seperable DE dx in x and z by using the…

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Q: 2- Linear edluan 1 - y' +スリ= 2é 2- x y'ony-ax? %3D 3. (x-2) y`+y. x 4 4-(49-3x)dX+5X dy = - 5_ dy dx…

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Q: Find the general soulution dy/dx=3y

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Q: The standard form of 3dy-xydx= 3y%e*/3 by Bernoull's equation is: dx A Зе dy xy = 3e**/3,3 dx 3 x-…

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Q: d In x Work out the following transformations (recall dx 1 ): dy d In x dy dy %3D dx dy -T² dT…

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Q: 4. Use Green's Theorem to evaluate | xy dx + (1 – xy°) dy where C is shown C below. y (1,4) (-1,2)…

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Q: Find dy du du dx dy when y and u are defined as follows. dx u = 3x - 9x² and y = √u

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Q: se Green's Theorem to evaluate SC (5y-9x)dy-(yx-x³)dx where C is shown below

A: Follow the procedure given below.

Q: Q.3 a) Verify Green's theorem for |(x2 + 2xy) dx + (y? + x³y) dy Where c is a square with vertices…

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Q: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

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Q: Which of the following is a Bernoulli's Equation? y^2 dx + (3xy + y^2 - 1) dy = 0 y (x^3 x^xy) dx…

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Q: Which of the following is not an exact DE? O (xy^2 + x)dx + (yx^2) dy = 0 O (2xy – 3x^2)dx + (x^3 -…

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Q: Question 13 Consider the integral dx. Using u-substitution, what is the appropriate u and du? 2e…

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Q: Use Green's Theorem to evaluate ya dz – x dy where C is shown below. Left Half of (0,5) x*+y = 25

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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: d*y _2d'y dx d²y_gdy +4y = 0. dx dx dx Ans.: y= (C, +C,x)e* +C, cos 2.x + C, sin2x.

A: Given the homogeneous linear differential equation with constant coefficient is…

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: Find dy du dy and when y and u are defined as follows. du dx dx y = 3u² + 6 and _u = x² + 2

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Q: 3. Given: y = f (u) and u = g(x), find dy/dx: a) у%3D сos u, и%3D—х/3 b) y = tan u, u = 10x – 5 - с)…

A: Our aim is to find the derivative of the above expressions.

Q: @ Consider the DE, dx %3D dt x (2t -7) What meho can be uoed

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: dy = 1+ xy dx is not separable. ylgn ihi

A: True.

Q: dy 3. da + y = 2xy?e"

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Q: Use Green's Theorem to evaluate Se xy dx + (1 – æy³) dy where C is shown below y (1,4) (-1,2) 2 1…

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Q: If z + In(e³x – e + e²) = 0 %3D - find dx at the point (0, 0)

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Q: Scy dx –x dy; C is the cardioid r=1- cos 0.

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Q: What is the point of intersection of the given 3y + x – 5)dx – (x – y – 1)dy = 0 (-1/2, -3/2) O (2,…

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Q: Question 9 e* What is the integrable form of dx? (A @ /(1-u²) 12 du [(u?-1) -12 du 1/2 du (D 2- 1)…

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

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Q: xy*-dy = (a* lIn a – y (а* In a - y %3D

A: we have to find the differential of ax=y

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

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Q: Assume x and y are functions of t. Evaluate DY/DT for 4xy-4x + 6y^3 = -258, with the conditions…

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Q: -a+ito + DNE - 十→f -2 1 DNE + DNE - -1 DNE DNE | -1 1 2.

A: The function f is increasing on some interval, if f'>0 on that interval.    The function f is…

Q: If we have to check the DE (5-8y+4xy)dx = (x+2)²dy for Exact then My

A: M dx + N dy =0

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.