5. Integrate: S (cose-sin8) de sec 20 6. Find f(3y – y³)ž(1 – y?)dy

Q: Evaluate the line integral / (9x + 10y)dx + (5x – 6y)dy along the curve C : a = 6 cos t, y = 12 sint…

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Q: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…

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Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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Q: 5. If the function y = y(x) is such that dy + 2y = x cos r, dr use the integrating-factor method to…

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Q: Find dz/dx and dz/dy for: x² sin (y³) + xe32 – cos(z²) = 3y – 6z + 8

A: Here, the given equation is: x2sin(y3)+xe3z-cos(z2)=3y-6z+8...(1) So, z is a function of x and y

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: dy 1. dx x(2 In x+1) siny+y cos y

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

Q: Let y = tan(5z + 6). Find the differential dy when a = 4 and dæ 0.1 %3D Find the differential dy…

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Q: Evaluate the line integral / (7x + 5y)dx + (3x – 9y)dy along the - curve C: x =2 cos t, y = 4 sin t…

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Q: 11) (3ycos(3x)dx– sin(3x)dy)/ y = 0 12) sin(ß y)dx =-ß cos(B y)dy

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Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

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Q: (. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

A: 19. f(x, y)=sin(x2)+cos y At π2, 0, fπ2, 0=sinπ22+cos 0                =sinπ4+cos 0…

Q: dy 4 – 5y = e-3t sin(4t) ; y (0) = 3, y (0) = 10 dy %3D - dt?

A: We solve the given IVP  y"-4y'-5y=e-3tsin(4t)........(1) y(0)=3, y'(0)=10.......(2)

Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, 4t2), o sts 1. (Round your answer to…

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Q: (cos y- zsee'y) de – sin y dy = 0

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Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. cos y A sin x B sinx cosy =…

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Q: Evaluate the line integral (5x + 8y)dx + (3x – 5y)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: Compute the differential dy for y = 7x° – 4x2. dy =||

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Q: Find the Wronskian for the differential equatio: dy dx2 fip dx 3 10y = 0

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Q: Find dw/ dt at t = 1 if w = xey + y sin z - cos z, x = 2sqrt(t), y = t - 1 + ln t, and z = pt.

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Q: Let y = tan(3r + 4). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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Q: Compute the differential dy for y = 4x³ + 2x?. dy =0

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Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: 2 1 Evaluate the iterated integral42x°y® dy dx. 56 -1 0 2 1 | 12*y®dy dx= [ -1 0

A: Consider the integral

Q: Evaluate the line integral / (6x + 8y)dx + (4x – 8y)dy along the curve C: x = 2 cos t, y = 4 sint…

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Q: Find y', where t (a) y = Jo dt VE2 +1 (b) y /t² +t+1 dt 1 • sin²3x (c) y = | 1 dt t2 +1 Cos x

A: The given function is: y=∫cos xsin2(3x) 1t2+1 dt

Q: b) Differentiate y = e (In3x) + tan (3y) with respect to x. %3D + 2e In 3x Ans: dy %3D 3 1-

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Q: The Integrating Factor for the DE y dx = (ye' – 2x)dy %3D is: -2y レマ None of These 2y

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Q: Given that y + x + cos(xy) = 0. Show that dy/dx = ysin(xy)-1 /1-xsin(xy)

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Q: 3. Integrate! 12e dt a) ] 5e041 -0.21 b) c) f- dx 6r dr 3r? .$1+ In 3x² d) [Vcot*0 •csc² 0 do 2+…

A: Using Methods Of Integration

Q: (1 + cos 2y) dr - 2r dy = 0, y(1) = i %3D Oy = Arctan 2 O y = Arctan O y = Arctan ( 1) D y = Arctan…

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Q: dz az B. Find əx and ay 3. x eY+ cos xy36xz+5x²

A: partial derivative

Q: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the T curve C : x = 10 cos t, y = 20 sin…

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Q: Q3: Find if: dx 2x dt sinx dt (1) y = (2) y = [ %3D t- 2 X cosx

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Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

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Q: What is the characteristic equation for dy 2. dt d²y y +2+e' sin 3t dt 2

A: Characteristic equation for the given differential equation:

Q: Evaluate the line integral / (2x + 7y)dx + (4x – 6y)dy along the curve C: = 6 cos t, y = 12 sin t…

A: Let's find.

Q: Find the differential of the function. y = V 4 + cos(0) -2 sin (0) dy V 4+ cos (0)

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Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

A: We need to evaluate integral.

Q: Explain, the given differential 3x²dx + 2yz dy + y² dz is exact or not.

A: We will check whether  3x^2dx+2yzdy+y^2dz is exact or not.

Q: Al/ compute 6(4+ ec©*) dx + (siny + 3x?)dy cosx Where c is closed bounded region lying in the first…

A: Given (A) The given integral is ∮4+ecosxdx+siny+3x2dy and the region lies in between x2+y2=4 and…

Q: Evaluate the line integral / (4x + 8y)d.x + (4x – 9y)dy along the curve C : x = 10 cos t, y = 20…

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Q: What is the integrating factor of the linear De of order one ydx + (2 – xy)dy= 0 ?

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Q: Can you help me step by step?

A: Given information:

Q: 1. Defermine the integrating thators of the pallo wing non- exnet exact esuations. A. (1+ 4xy -…

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Q: By (d) dy 2- = 3t + 2, y(0) = y'(0) = 0. dt By +4 dy + 20y = -3 sin 2t, y(0) = y'(0) = 0. (e) dr² dt…

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Q: What is the integrating factor of the nonexact DE (4xy + 3y – x) de + æ (x + 2y) dy = 0?

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Q: (2e" sin(y) – 4y)dr + (–7x - e cos(3)dy = 0 not exact

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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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