A point moves in the (x, y) plane on the line 2x+ 3y −4 = 0. Where will it be when the sum of the squares of its distances from (1, 0) and (−1, 0) is smallest?

Q: Give the general solution to the equation x' Ax where A = %3D

A: To find the general solution of the given system, first we find the eigenvalues and corresponding…

Q: у" - у' - 2sin 2x

A:

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: y" + y = 2x

A:

Q: 16. Of all points (x, y, z) that satisfy 3x + 4y + 2z = 52, find the one that minimizes (x – 1)2 +…

A: Let f(x,y,z)=x−12+y−42+z−22   and    g(x,y,z)=3x+4y+2z−52≡0Apply Lagrange Multiplier method to find…

Q: Find the formulation of a particular solution of y" + 3y' +2y = 3+t2 – te-2t cost without…

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Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = 2x3 + 3y2 + 1.

A: To verify that

Q: Differentiate the following linear and non-linear equations, and give a reason that why its linear…

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Q: x(1-х)у" - Зу' + 2у %3D0

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Q: Find the best quadratic approximation, Q(x, y) of V9 + 7x + 5y for (x, y) near (0,0), Q(x, y) :…

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Q: Find two nonnegative numbers x and y such that xy=72 and 9x+2y is minimized.

A: Let the two non negative numbers be x and y Given xy=72 Therefore, y=72x Sum of two positive numbers…

Q: Find the general solution for the homogenous equation of y′′ − y′ − y = 0.

A:

Q: state where in the ty-plane the hypotheses of Theorem are satisfied 7. y′=(t2+y2)3/2

A: Given y'=t2+y232

Q: If x < 0 and y > 0, determine the sign of the realnumber. x/y

A: It is given that, x < 0 and y > 0

Q: Is y(x) = C1sin2x + C2cos2x, where C1 and C2 are arbitrary constants, a solution of y” + 4y = 0?

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Q: Show that the equation x+y+z=4,2x+5y-2z=3,x+7y-7z=5 are not constant

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Q: If x < 0 and y > 0, determine the sign of the realnumber. xy2

A: Given that, x < 0 that is x is negative. y > 0 that is y is positive.

Q: 3. /4(1-)esc (1-y)dy

A: We have to solve the integral

Q: Solve for the orthogonal traectories y2= 4x²(1- kx) %3D

A:

Q: dz Find at (2, -2, 1) if x² + y? + z2 6xz + 6yz + 21

A: Given equation is x2+y2+z2=6xz+6yz+21 We have to find ∂z∂y at 2,-2,1

Q: Use Variation of Parameters to obtain the General Solution 1. y +4y 4-sx2x

A: Solve the given problem.

Q: y = Vx+6 y = v-x² – 4x |

A:

Q: Find the maximum value that f(x, y, z) = x² + 8y - z² can have on the line of intersection of the…

A: Given function is f(x,y,z)=x2+8y-z2 and the other constraints are g(x,y,z)=2x-yh(x,y,z)=y+3z We…

Q: x, prove that y¨= 2(y² +1)(3y² +1).

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Q: Find that solution of y’= 2(2x-y) which passes through the point (0,1). Use Linear Equation of Order…

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Q: variation of parameter

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Q: What is the general solution of xy^2dx+x^2ydy=0

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Q: Find two linearly independent solutions of y" + 3ry = 0 of the form Y1 = 1+ a3x³ + a6x® + · .. Y2 =…

A: We find two linearly independent solutions of the given differential equation  y"+3xy=0.......(1)

Q: find the maximum value that f(x, y, z) = x^2 + 2y - z^2 can have on the line of intersection of the…

A:

Q: Find the general solution of ди ди (y – z) + (x – z) ди + (2y – 2x) ду - az

A: The differential equation is given as (y-z)∂u∂x + (x-z)∂u∂y  + (2y-2x)∂u∂z = 0 We will solve it by…

Q: Find the equation of a line perpendicular to 3x – 2y = 16 that passes through the point (9, 4). - Oy…

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Q: Find the general solution of (3D2 + 5DD' - 2D'2)Z = 10 cosh(2x + 5y).

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Q: Obtain two linearly independent solutions valid near x = 0 x(1-x)y" - 3y' + 2y = 0

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Q: Solve for x,y,z:  3x +2y − z = − 1  − 2x − 2y +3z = 5 5x +2y − z = 3

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Q: Obtain two linearly independent solutions valid near x = 0  x(1 - x)y" - 3y' + 2y = 0

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Q: Obtain the general solution valid near the origin: 2y" + 9ху' — З6у %3D 0

A: Power series solution of the differential equation

Q: Solve for fazy for f(x, y, z) = 4x³y²z - e²zy¹ + + 4y - x¹6

A:

Q: If x < 0 and y > 0, determine the sign of the realnumber. x2y

A: Given, The real number is x2y.

Q: Find the solution of y-x =0 using separable variable method. dx

A:

Q: Find the particular solution of xy' – 2y = -x ; when x y = 5 1,

A: Recall: Consider the first differential equation                           dydx +P(x) y =Q(x)…

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: Obtain the solution using Integrating Factors Found by Inspection 2x 5y ′ = y(3x4+y2)

A:

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: Differentiate x²y3 - y2-6x=0 with respect tox. A 3x²y2-2y −6+2ху 3 2х3у2-2y - 6 6-2xy3 3ху2+у В С D…

A:

Q: Solve for y in terms of x and z. z = xy

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: Use the characteristics method to solve the problem U, +3yU, = 2U , U(x,1) = f(1+ x,)

A:

Q: Differentiate the following linear and non-linear equations, and give a reason that why its linear…

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: Find the general solution of the lines 3y (즉 + 2-2)dx + (2x- 3 +1 )dy = 0 - 2 )dx + ( 2x - +1 )dy =…

A: x2+3y4-2dx+2x-y2+1dy=0To Find: The general solution of the lines.

Q: Evaluate B: А: Vye-y° dy 3e-4z2 dz 0, 0,

A: There is a general integral that gets calculated with the help of β function. The integral is…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.