2.Linean ectuation 4-L4y-3x)dX+5Xdy=o 5.

Q: 3 wu= 2-x. [ w/2-xdx= If U = | x/2-x dx= 3 (2 – u)Jūdu Luūdu -1 .3 uſudu D (2 – u)Vūdu -1

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Q: 5 If u =x² +y² and v = 4xy, determine дх дх ду ду du' dv' du' dv

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Q: 2 al S ex+y dydx

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Q: € 4. If y=u² and u = x³ + 4 determine dx

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Q: 7. Evaluate. LL sin z da dy.

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Q: 5. St V1-t dt

A: We solve this integration by substitution method by putting                         1 - t3 = u…

Q: solve the intial value problem y'' + 6y' + 9 = 0 , y(0)=2 , y'(0)=-5

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Q: 26. у" + 4y' %3D sec 2x

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Q: .3 , Ry* In y dy

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Q: 2. If y = x2 + 2 and u = 2x – 1, then du II

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Q: (in) S 15:22 15-z dx. u = (M S 15 - TV9 – a² dx. u= (vi) S dr. u = 22+15

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Q: In 8 In y S S e*y dxdy x+y

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Q: dy (y2+In2)=-(23+) %3|

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Q: , where a, B,Y

A: Let f(x)=αx2+βx+γ be a function defined on the closed interval [a,b], where α,β,γ,a,b are real…

Q: 4. Evatuate E Jitxe dx dy answered you to draw.

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Q: | (h(y) – 4)dy = 18 h(y) 9(y) 1 |dy 19 12 15 18 - 18 - 7g(y)dy = 1

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Q: 2- Find the solution of the diff. equ. dy ty Six dx

A: First Order differential equation :        Consider the differential equation…

Q: 19. MZPQR S 313 R (25x-13)", %3D

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Q: 2 If [ In(ax)dx = 4, then a = 1 es 4 O None eo 4 e4 4 4

A: Basics of Integration are used.

Q: 11. (4+ t) dt 13. | – 5y) dy 15. (31² – 4t + 5) dt

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Q: 1: find af/ox and af/ày.. ) (x, y) = Vx² + y²

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Q: Find the most general antiderivative. Sex.6x+ 4) dx O 6x2 +6+ C (2x3 O 6x+12x+4x+ C 14+3x2+4x+ C…

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Q: 7. If (x, y, 2) = 3xz³y – y?, find grad o at the point (1, -2, –1) Ans. - (16î + 9j + 4k)

A: The gradient of a scaler point function φ is obtained by applying the del operator ∇ to the scaler…

Q: 4. Show that (1) SST = Cu – 9)* = vy - ng = v (1. -) (2) sSR= Em – )* = ³ X'y – ng° = v ( H - )v (3)…

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

Q: 2Iny dy ,2Iny coth e S y csche?y coth e

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Q: .1//3 7earctan(y) dy + y? 3

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Q: 3. If z* +x²z+z+y = 0 find (1) Əz/ax, (2) əz/əy, (3) ²z/dx², (4) d²z/@y², (5) Fz/dxəy, and (6)…

A: As per our guidelines, I am only solving the first three. For other kindly upload the question…

Q: EXAMPLE 4: WY = In AWXY: WX = 9 m, XY = 15 m, and n ZW =31° m2X = mZY =

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Q: B) fometie w= xty+y2-23, x²ry*+2?=6

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

Q: Creular Decaululiom x/lyecn)= [3,5, 4), X= [1,2,1] Tad han)? 1 2. 2, + 3.

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Q: 2 If [ In(ax)dx = 4, then a = 1 es 4 O None e6 4 e3 4

A: e^5 / 4

Q: 9. S(9 + 8y – y²)= dy

A: Topic = Integration As per guidelines , At  a time only one question can be answered . please repost…

Q: O y'+ (oy -asin 8t y W): -1 2

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Q: 25 -x2 -dx, if we let u=/25 – x? , then udu =- xdx. In A) True B) False

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Q: J Ax) dx 11. 12. -3

A: 11) From 0 to 5 there is a trapezium and from 5 to 6 there is a triangle

Q: 3. Obt nin the parh cular folu tion 9. xdx - ydx + 3x dy +ydy = 0 ; wun x - 5,4= -:

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

Q: Evaluate     C(y − x) dx + (4x + 7y) dy. C: line segments from (0, 0) to (4, −8) and (4, −8) to (8,…

A: Given data-   ∫C(y − x) dx + (4x + 7y) dy. Where, C: line segments from (0, 0) to (4, −8) and (4,…

Q: If s = 4/t - 3, then %3D ds dt

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Q: لله √ √³ √ √² zysin(2² + y²) dz dy −

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Q: S(6 + 6y – y²) dy

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Q: 5 10-2z 12y – 8x dy dæ dz

A: To solve the triple integral

Q: 1. аєL; VxeL xb,ха,bx€L 5. ає L; VxєL xb,ах,bx€L 5. ає L; Wx€L xb,xbaєL

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Q: 39. If z = 5x² + y² and (x, y) changes from (1, 2) to (1.05, 2.1), compare the values of Az and dz.

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Q: • In 2 cV(In 2)²-y² R+y° dx d

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Q: 2/3 If y = xl/3 + 2 dy then |z */0 =-8 dr

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Q: 2 If [ In(ax)dx = 3, then a = %3D es 4 e4 4 O None e3 4 e6 4

A: Given that: ∫12lnaxdx=3

Q: 16 Find Ehe eract length of Ene eurve, /2 x= e- 4E, y= Re O<6< 2

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Q: 3. Evaluate S, 2y²sinxy dy dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: ф%3 ASin2лut $ = TUt dø, k " ø = 0 dr m U = ? +

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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.