Describe the long run behavior of f(r) = – 5r° + 2r - 3r2 + 3

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

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Q: Find the solution of the DE using variation of Parameters y''' - 3y'' + 3y = (ex/x)

A: The given problem is to find the solution of differential equation using method of variation of…

Q: Is the function y = Cx2 a solution to the ODE y''- xy'+y=0?

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Q: nd the general Solution of the tfferential equation. (x+2y-1)dx+(3x (3x+by)dy = C

A: The differential equation is given as , x+2y-1dx+3x+6ydy=0. Simplify the differential equation,…

Q: Find d2y/dx2 in terms of x and y. x2y2-10x=1

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Q: d²y Solve the particular solution for = 2 – 4x when points (0, 2) and (-1, 3) are on the dx2 curve.

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Q: Find the linearization of-ƒ(x, y) = x2 - xy + 1- 2 y2 + 3?

A: Here we have,  f(x,y) = x2-xy+1-12y2+3 at (3,2)

Q: Show that the relation y^2 - x^3 + 8 = 0 implicitly defines a solution to the nonlinear equation…

A: The given data is: y2-x3+8=0

Q: Solve by Chain Rule f(y) = /2y + (3y + 4y²)³

A: Given that       f(y) = √{2y+(3y+4y2)3}

Q: Find the y(t) if Y(s) = 3+1

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Q: Solve the nonhomogeneous ODE. y" - 6y' + 9y =x²e5x

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Q: Solve the non-homo. D.E. 1.y" + y = 3e2x

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Q: In(ax) f(x) has a stationary point at Find a and b. bx 2' 3e,

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Q: Find d²y if y =x² +3x-7 and x=2t+1. dt?

A: y=x2+3x-7 and x=2t+1

Q: Y Is the midpolnt of XZ.If XZ 8x-4 and YZ = 3x +1, find x.

A: Given Y is the mid-point of line segment XZ XZ = 8x-4 YZ = 3x+1   to solve the given question use…

Q: y'' - 6y' + 9y = x^-2(e^3x) using Methods of Variation of Parameters

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Q: Determine exact solutions for the equation 2sin2x-3sinx + 1 = 0 in the interval x e [T, 3n].

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Q: Eo f is y = 1(a- 4). 3D1

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Q: Q1) find the critical point of the following equation - g(x, y) = x² + y² + 2xy − 6x - 3y + 4

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Q: find the general equation of : x^3dy+xydx=x^2dy+2ydx  ;y=e when x=2

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Q: a. Solve f'(8) for y = Vx – 4x-1 + 2x x² – 6x + 9 b.The y'for y = x – 3 c. The f'(3) for y = v3x² +9

A: Given: a) y=x3-4x-1+2xb) y=x2-6x+9x-3c) y=3x2+9

Q: 2 c4 e-x-2y dydx 2х

A: It is double integration problem

Q: 2 Find dyif y.+3x-7 and x =, 2t +1

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: Q16// find the general solution (cosx)y²dx + 2ysinx dy = 0

A: I

Q: t² - t dt 0, = (x)6 g'(4) =

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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: Q2\A: By using partial method solve 2x² cos x dx

A: Given :∫2x3cosxdx

Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

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Q: I Sdve for dy using the four-step rule 2. y = x"- x 5X-3 ソ= 4- 3X

A: We have to solve the problem

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: j. f'(2) appears to have a value of

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Q: T:4x-34+2-2-0 Tz: dx+ Sy-32+4 = 0

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

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

Q: Solve by Chain Rule f(y) = /2y + (3y+ 4y²)³

A: Chain Rule of differentiation :      If f(y) and g(y) both are differentiable function and F(y) is…

Q: The equation f(x)= x² -e* has a solution [-1, 1]. With po= -1 p1=1, calculate p2 using the the…

A: The secant method uses the formula: xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn) to perform the iteration. The…

Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: Determine the orthogonal trajectories for x2 = ky³. A) 2x2 + 3y2 = c C) 2x2 – 3y? = C - D1.2

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Q: f(x, y) = 6 – V4 - x2 - y2 is

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Q: Q3) a) find f sec³ x dx

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Q: The y, of y'"-y=2x²-x -3 by using variation of parameters is: .A y,(x)=Ae*+ Be- .B Yp(x) = x – 1 .C…

A: Given that  y"-y=2x^2-x-3 To find the particular solution by using the variation of parameters

Q: dy Find the general solution of xy + y² dr x2

A: According to our guideline, we can solve only first question of multiple question.So, here we solve…

Q: Is the equation t²y' (1) t + 4 - separable? y?

A: t2y't=t+4y2

Q: -3x2 F(x) = S*" t² dt %3D

A: TO EVALUATE THE FOLLOWING INTEGRAL F(x) ∫-x3x2 t2 dt FORMULA USED- ∫abxn dx = xn+1n+1 i.e substitue…

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: Find the general solution of y" = 6y' – 9y where y is a function of x.

A: Given differential equation, y''=6y'-9y Find the general solution of the differential equation.

Q: Find the equation of a line parallel to x = -8+ 2y that passes through the point (8, –2). Oy = -x –…

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Q: Find DF of fcx,y)=x²e° at the point (-2,0)-

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