(d) / VI- 40² dæ dt (e)/ Vt² -6t + 13 | Hint: If you complete the square, t2 – 6t + 13 = (t - 3)2 + 22. Use the substitution t- 3= 2 tan %3D

Q: Find the general solution of thedifferential equation. (2+x)y'=3y

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Q: dP 5. = P- p2 cet Ans: %3D %3D dt 1-P

A: topic - differential  equation

Q: Show that the equation of the tangent line to the hyperbola                        x2/a2 − y2/b2 = 1…

A: Given Data The equation of the hyperbola is x²/ a²- y²/ b²=1. The points are (x0,y0).…

Q: from y = ae + be %3D 2.

A: y=ae4x+be-4x ....(1) Differentiate both side w.r.t x dydx=4ae4x-be-4x        ....(2) From (1) and…

Q: y' + z' - 2y = 1 z – y' = t %3D Yo = 20 = 1 %3D -

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Q: Find the solution. (D5 - 2D3 - 2D2- 3D - 2)y = 0. -3x y = (c,+c,x)e-*+c;e-+e*(c,cosx+c gsinxr) -2x A…

A: Given differential equation is (D5-2D3-2D2-3D-2)y = 0

Q: a) sec²t + dt 2 + V5 b) ys – 2y c) - dy

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Q: Čonvert the following equation into standard form. 7x y = - - 3 %3D 2 [?]x+ [ ]y = [ ]

A: The given equation is y=-7x2-3

Q: ux.ュメトXス1いスコ-Y Palx, utェッズ)-。 入2コメ; +メュ-」+5- メレ 2 d、しズuメッ]= xit Xzメ]-6 fnd in Ganeral rm.

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Q: Find the linear approximation at x = 0 to Write %3D 2- your answer in the form y = Ax + B. %3D

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Q: dx -2xcsc 2y – 2x³cos 2y dy sec 2y

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Q: 1. (D³ + 3D² - 4D - 12)y = 0 2. - d'x 19+ 30 = 0 dt3 dt 3. (4D4 - 8D³ - 7D² + 11D + 6)y = 0

A: 1). From the given differential equation; D3+3D2-4D-12y=0 So, The auxiliary equation is:…

Q: An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at…

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Q: Ex(4) A particle moves from point (-2,5) to y-axis in such a way that Ay = 3Ax. Find its new…

A: Solution is given below:

Q: 10et --2 Use lap lay trensform system dy, to find the solution of the 1 dx -24, + Y3 +Y2 XP

A: Given system is dy1dx-y2=04y1+dy2dx-4y2-2y3=0-2y1+y2+dy3dx+y3=0 From the first equation of the…

Q: Find x and y in terms of a. X + y = 0 х+ ay %3D 6 (а + 1) (х, у) —

A: Given:    x + y =0        --------1   x + ay = 6     --------2 from 1: x = -y put the value of x in…

Q: 1 Oy' = %3D xsiny+2sin2y

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Q: Find the general solution of: ydx — х*dy 3D0. || -

A: Use variable separable to solve the differential equation. Note: We are allowed to solve one…

Q: et 2e-2x - 3e2x V3 Arcsin 6. A +C V3e2x + C V2 B Arcsin 1 3e2K+- +/3e4x 2+C 1+c - 23

A: Given integral is ∫ex2e-2x - 3e2xdx

Q: dy = -1-yy2Yュ- GD %3D

A: Given

Q: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: At the point AI 2.4) was rotated counterclockwise A. LTS image would be located at 13 A'L 4-2) (21…

A: Let us take a random point x,y. If x,y is rotated counterclockwise by 90°, then the co-ordinates of…

Q: Dyy 2y-x; %3D

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Q: 3. (D2 + 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

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Q: Solve using D-Operator 3. y + 2y + y = x²

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Q: y = VT, y = 2 - x and r O about the x-axis?

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Q: 2. Determine C when x-y%3D0 show the solutions. (xy + x)dx = (x²y2 + x² + y2 + 1)dy

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Q: Find dy2 of z = 2x – 5xy² + x² y° %3D -

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Q: (A)A particle is moving in a straight line according to the formula s(t) = 2t³ – 9t² + 12t – 15 .…

A: To determine: A particle is moving in a straight line according to the formula:…

Q: in yy = 2 y-x; %3D

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Q: Use the diffecential equation dy= and the initial condition. y=(9)%3T. Fad funchion of 81.

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Q: + %3D 5 -11 3z -4 N N N

A: 2w+3x-4y+z=9...........(1) w-3x+y-z=5.................(2) -2w-x-3y+z=-11........(3)…

Q: Find the point on the line y = 4x + 3 that is closest to the origin. %3D (x, y) = %3D -

A: Given query is to find the Indicated point .

Q: Find the veeton equation of a Line L going thagh the P= C-6,2) $ paeallel to the ine point %3D…

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Q: 8r2 te V1-4.a

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Q: Is the equation y '(t) = 2y - t separable?

A: Given a differential equation, y't=2y-t

Q: Find the Direcctional derivatve of the function foxxy,z)=tan(xjz) aut point (t,2,4) in the direction…

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Q: Show that the equation of the tangent line to the hyperbola x2/a2 − y2/b2 = 1 at (x0, y0) is x0x/a2…

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Q: dy of y3Dx dr Find csc2r,

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Q: Graph the curve. O r = 6 + sin(40) -6 -4 -4 y 2 2 4 4 X BB÷ 2 4 -6 -4 -2 -4 -2 2 -6 2 4 6 X

A: The given function is r=6+sin4θ To find: We have to find the graph of the given function. We have…

Q: dy un 3 sec2 5x, w dr

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Q: (бх - Зу +2)dk - (2xх - у -1) dy 3D0 |

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Q: у 3D sec u аnd и — е 2х — 4 csc x -

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Q: y = mx + b is called the v ---Select--- rm of the equation of a line. standard Additional Materials

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Q: A particle moves on a vertical line so that its coordinate at time t is y=t3 - 12t + 3 , t>0. When…

A: (b)        y = t3 -12t+3    y1 =3t2 - 12 = v(t) when particle moving up means v(t)>0    3t2…

Q: d³r dz +t- dt3 (c) 4tx = 0 %3D dt

A: The solution is given as

Q: u³ = a²t , find d’u %3D dt3 2a4 а. 9u5 10a6 27u8 -10a6 С. Zu® 40a6 d. U8 b.

A: A detailed solution is given below

Q: Solve the dff oq dy 3x寸票-5-2 %3D

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Q: dx Calculate for n = 6, using trapezoidal rule. %3D -11+ x²

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Q: Show that Y, CX) = x is one of this functio %3D Solutions: x*y" + 2 xy' - 2 = 0

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