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: Determine the particular solution. (2xy)dx = (y² – x²)dy × = 1, y = -2 2 = 3x3y + y3 O 3 = 3x?y + y3…

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Q: (c) y?r dy dx 22

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

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Q: The function f (x,y) = e* +3 tan – is a homogeneous function of degree_

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Q: tan(v) In(cos(v))dv.

A: Assume lncosv = t Differentiate both sides

Q: Evaluate y sin(xy) dA, where R = [1, 2] × [0, π]. R

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Q: H.w: find dy dx 1- y=-10x+3cosx

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Q: solve D.E. by using homo. xsin-- ycos-) dx + xcos-dy = o

A: put y=vx dydx=v+xdvdx differential form  v+xdvdx=vxcosv-xsinvxcosv take x common and split the…

Q: Which of the following equations is NOT an exact equation OA. (2x sin y + y)dx + (x² cos y + x)dy =…

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Q: J cos 3x cos 4x dx :

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Q: Find dx. Using the substitution u=3 – 2x (3— 2л)5 |

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Q: 10 10 -1 If the sum tan (m + 4) b=1 a=1 (1) = mл, then find the value of

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Q: Ss(-y+ye=y)dx + (x + xeªy)dy,

A: Given data:     The given integral is: .   The expression for the Green’s theorem is, Compare it…

Q: If dy = x cos x² and y = -3 when x = 0, when x = π, y = -3.215 2 1.647 6

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Q: Hiw. Solune the PDE: (D% - 4Dx Dy+ 3 Dg )u = e Cos (2x+y)

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Q: Which of the following equations is an exact DE? A (x²+1) dx - xy dy = 0 (B) x dy + (3x-2y) dx = 0…

A: Exact and non exact differential equations

Q: dy dx2 in terms of x and y. Find x2y2 - 4x = 3 dy dx2

A: Given equation :

Q: 3-Evaluate S Fdr where 2X Cisgiven by rT) = C 3+U-3t)jrék

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Q: Use Greens Theorem to evalute fyx² dx + x²dy as shown below Leh Half of (0,5) +y-25 (0,-5)

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Q: nd the tallawing differentu equation =d -1Sx +7 +eX cos(3x). the beral

A: The general solution of the given question has been solved below.

Q: (4e²+7x°+5 cos z + 2)dx

A: Solve integration

Q: Evaluate: (4) S esc" (a) (2x +1) dx C6) Syos y dy

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Q: S cos(3x – 2n) cos (x + t) dx

A: We know that, 2cosAcosB=cos(A+B)+cos(A-B) Also, ∫cosxdx=sinx

Q: 1- dX dy (bux> dy 2- dx : 2X Secy 3. (1-x"): - 2Y dy

A: Answer 1 -  As the cube root of 64 is 4, thus open the parentheses of the RHS of the differential…

Q: dx x dyx+(1+x7y}=12

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Q: 1. Evaluate: 2. Evaluate: 3. Find dy dr d dx d dx [√√5 + (x6 + 1)³ [cos¹ x + sin¹ x] for: (x² + y)³…

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Q: Use linear approximation, i.e. the tangent line, to approximate ✓125.1 as follows: Let f(x) = = V.…

A: For the  function f(x), the tangent equation at x=a Is given by  y=f(a) +f'(a) (x-a)  given that…

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.