E(x,y) = 3x²+2= -6x+ &y+I6

Q: Apply Euler-Cauchy Runge-Kutta method for the equation: 2y t y (1) = 1 y' = and cbtain У, , Уг and y…

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy + y?

A: Idea: after separating x,dx and y, dy terms together. we take integration on both sides . after…

Q: y" - 6y' + qy 2,

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Q: x(x – 2)y" + 2(x – 1)y' – 2y = 0

A: Solution: x(x-2)y"+2(x-1)y'-2y=0 Solve using the series method: A linear homogeneous ODE with…

Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

Q: Use separation of variables to find an explicit solution. xyy' = 2xy² + y² %3D

A: Follow the steps below to solve a differential equation by the variable separation method. First,…

Q: Vx? + yZ 49x2 49 [F,(x, y)]² + [f,(x, y)]² 1+ x² + y2 e have [f,(x, y)]² + [f,(x, y)]² = /

A: This is the question from vector calculus.

Q: Maximize Q = xy, where x and y are positive numbers such that x+3y 16. The maximum value of Q is and…

A: Maximize Q=xy, where x and y are positive numbers such that x+3y2=16

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

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Q: Solve for x, y, z and w by Gauss elemination Method. Given: 12x-8y+6z+10w=26

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Q: Solve for the antiderivative of the function f(x) = C. *++3x + C A. ++9x+C B. 즉++9x +C D. 2x ++3x +…

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Q: Find y(3) for y' = 1 + (x-y)2, y(2) = 1 by using Improved Euller's method. h = 0.5

A: Given  y'=1+x-y2 y2=1, h=0.5 We will find the value of y3

Q: use Separation of Variables to find the general solution. yy' = x

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Q: Solve the following equation by using separation variable method: y(x,0)=10 t> 0 y, (0,1) = y,(7,t)=…

A: The given problem is to solve the given partial differential equation with given initial conditions…

Q: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: Find general solution of y" – 2y' + y = , By Variation of t2+1' parameter method.

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Q: Find the general solution by using reduction of order method to (x2 + 1)y" – 2xy' + 2y = 0 given…

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Q: Find the solution (varition of parameter)   X2y11-2xy1+2y=x3sin x

A: According to the given information, it is required to find the solution of the given differential…

Q: y" -4y' + 13y :

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Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 3e* Y,(t) =|

A: The given differential equation is  y"-y'-6y=3e3t  We have to find the particular solution of the…

Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: Find V x F for F(x, y, z)= - -xZ + y² i+ -yz x² + y² =j+√x² + y²k.

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Q: Find the general solution of y" – y' – 2y = cosh 2t.

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

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Q: V Solve usinog variaton of parameters or reduction of order (D²- 2D+1) y = e2"(e*+1)?

A: Solve by using variation of parameter  find auxiliary equation and then find wronskian and put in…

Q: (a) x² + zsen xyz = 0

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Q: Let f (x, y) = r³ + y? – critical points of f . 4xy + 3x + 2y+5. Find and classify all

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Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

Q: Find and classify the critical points of f(r, y) = 2y²x- ya? + 4yx.

A: Here we have to find and classify the critical points of f(x,y) = 2y2x - yx2 +4yx .

Q: g(x,y)=y-x2=0 depending on the condition f(x,y) = x2+y2-6x+9   can you find with the lagrange method…

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Q: 1- , L, v² e*dydx 2- S S マーーー ydxdzdy a>0

A: Explanation of the solution is given below...

Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

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Q: Let y = v2x. Determine the point (x, y) that is closest to the point (5, 0). That is, deteremine the…

A: find the minimum distance from a point

Q: SS x dxdy 2 x OSSydydx 2 ®SS_- ydz 1+Vx+y -1-VI-2

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

Q: C(x, y, z) = 90 + 6x + 4y + z where x is the cost of 1 pound of one raw material, y is the cost of 1…

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Q: x² + y² = (2x² + 2y² – x)', (0,¿), (cardioid) -

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Q: Let ulx) be the solution of the IuP xy'-2y:x, yQ)=0 Evaluate y(32) %3D

A: In the question we have to find y(32).

Q: Use Midpoint method dy dr 1 1 reš - 2y, 0<r <1, y(0) = 0 with step size h = 0.5 and the actual…

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

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Q: Use one step of Euler’s method to approximate y(0.1 + π/4 ) if y′ = xsin(x + y) and y( π/4 ) = 0.

A: Use Euler method

Q: Solve the DE using Linear First Oder Method: y +yx = x - 3. if y(0) = 2 %3D

A: Given y'+yx=x-3   if y0=2 To find the general solution

Q: hich vect וdtiolו y and 2? 1 -2 y = 1 -6 x = 2 8 -1 2 -1 5 2 -3 [ 2 -1

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Q: y +y² – 1 = 0, Yı = 1

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Q: 1 y" – 2y' + 2y y(4) = 0, 3 (4) = 0. -

A: Given: The given differential equation is y''-2y'+2y=1x, y4=0,y'4=0

Q: 1. f (x, y, z) = x° ỹ + 4z°y² – xyz + x² – Vz -

A: Given that: f(x, y, z)=x3y+4z3y2-xyz+x2-z53               NOTE: As per our answering guidelines, we…

Q: Find general Solution of y + +y+ 4y = Ct1)e Using method of vanafion.

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Q: © f(X,y) = x4 + 'onY -10 © w = x*y - 10yZ z³ + 43X – 7tan (4Y)

A: It is partial derivative

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

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