Find the stationary points of the autonomous equation x˙ = x2 − 4x4. Classify each stationary point as stable, unstable or semistable

Q: 7x – 4xy = C

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A: Given  x= ln(6t) y=t2

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Q: 2x Find the orthogonal trajectories of the family of curves y = Ce" .

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Q: Find the orthogonal trajectories of y = ae" where a be the arbitrary constant.

A: The objective is to find the orthogonal trajectory of y=aex, where a be the arbitrary constant.…

Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) 2y³ + 3x² = C (F) 2y³ + x³…

A: Introduction: An orthogonal trajectory of the family is any curve that cuts each member of a…

Q: The cartesian equation of the curve x = VE .y 1-t is :

A: The characterstics eqaution of the curve is

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

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Q: utwards from the point (0 nd S, the top half of the

A: Given, the vector field                        E(x, y, z)=x, y, z-3this vector field can be…

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Q: Given the equation: (x² + x – 2) y" + (x + 1) y' + 2y = 0, - find the singular points and determine…

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Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: Find the orthogonal trajectories of the family of curves x when 'a' is the parameter. +y Da

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Q: Find the orthogonal trajectories of the family of curves x² - y² = (² A x² + y²=C² B) xy=C (C) x-y=C…

A: We can solve as follows

Q: Find the orthogonal trajectories of the family of hyperbolas xy = c

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Q: y' = y– y³e=2x у — узе-2х

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: Find the orthogonal trajectories of the family of curves x²- y2=C² A) x- y=C (B xy3=C xy=C D…

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Q: Find and determine type of stationary point for ƒ(x,y)=x' – 3x² + 2xy – y

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Q: Eliminate the parameter to obtain an equation in x and y: x=-2cos2t, y=-2sin2t

A: x=-2cos2t y=-2sin2t using trigonometric property,               sin2t+cos2t=1

Q: A parabola has the equation y^2 = -4ax. Determine the slope of the orthogonal trajectories. 2x/y O…

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Q: Find the point on the curve y = Vx closest to the point (1,0).

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Q: Find the exact length of the curve y = In(1 – x²), 0 Sx S

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Q: Trace the curve r2 = 4cos etan2e. %3D

A: The given equation is r2=4cos4θtan2θ. Simplify r2=4cos4θtan2θ as follows:…

Q: Eliminate the parameter to find a cartesian equation of the curve x = t4, y = ln(t)

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: Give the family of orthogonal trajectories for the equation: y2 = Cx5+5

A: To obtain the family of orthogonal trajectories for the equation: y2 = Cx5+5. Find a differential…

Q: y6 = C (x² + 1) %3D

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Q: A particle travels along the parabola y = ax^2 + x + b. At what point do its abscissa and ordinate…

A: Given: y=ax2+x+b

Q: find the equation of the secant lines of y=√x passing through the points: x1=1 and x2=2

A: Secant line for a function between two points on a curve is simply a straight line passing through…

Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

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Q: Eliminate the parameter to find a Cartesian equation of the curve for −2 ≤ y ≤ 4. x = t2 − 3,…

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Q: Find the Orthogonal Trajectories: a.) y6 = C (x2 + 1)

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Q: Find the orthogonal trajectories of У — сх CX

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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: Two particles move along the spatial curves r1(t) = (t, t2, t3) and r2(t) = (1 + 2t, 1 + 6t, 1 +…

A: In the question it is given that- r1(t)=t,t2,t3  and r2(t)=1+2t,1+6t,1+14t represents the spatial…

Q: 4) Find the orthogonal trajectories of the family of parabolas y – 3 = c(x + 1)².

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Q: (c) Given that y = x4 – 8x²

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Q: ind the orthogonal trajectories of the family of curve x2/3 +y2/3 =a2/3 where "a" is the parameter

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Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

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Q: Find and determine type of stationary point for f(x,y)= 2x² – 4.xy + y² +x+3y

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Q: Find the orthogonal trajectories of curves represented by x = Cev Select the correct response: y =…

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Q: Find the orthogonal trajectories of the given family of curves y? = tcx 1-cx

A: The orthogonal trajectory is the family of curves that is perpendicular to the given curve. The…

Q: Find the orthogonal trajectories of a system. x'y2- 2xya + a2 0 %3D

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Q: 1 Find the stationary points and state the nature of the curve y=xe.

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