Find the point thot maximites the f (xxy)= x*+ y 2. -6x+ 9 funcfion depending on the gCxy) zy -x² condition with 2. the Lagrange method.

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: Depending on the condition of g(x, y) = y-x2 = 0,  find the point that maximizes the function of…

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Q: Q2: Find y(0.2) fory' = -2x - y, y(0) = -1, with step length (h) 0.1 using Second order Runge-Kutta…

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Q: 3x* – 4y* = C

A: The given equation is: 3x4-4y4=c

Q: use the Lagrangian method to solve:   U=(x+3)(y+5) given 30=3x+2y

A: Given the relation 30=3x+2y. We need to minimize the value of U = (x+3)(y+5). Substitute the value…

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) =…

A: The function fx,y=11-3x-y Then the taylor's formula for fx,y is, fxx,y=31-3x-y2fyx,y=11-3x-y2 Then…

Q: (B) Find the solution of f(z) = x'+6x'y+i 3x'y by using Cauchy-Riemann method

A: we have to solve the given problem

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

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

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

Q: Find the extreme values of f(x, y) = x² + 2y² subject to xy = 4 using Lagrange multiplier method.…

A: Here we have to use the Lagrange multiper method

Q: a. My =n xyy

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Q: Apply Euler-Cauchy Runge-Kutta method for the equation: and obtain y' = 29 t y (1) =1 y, y, and y. 3…

A: Hint: Formula for finding n-th approximate solution of IVP  dydx=f(x,y), y(x0)=y0  is…

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

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Q: Let y(x) be the solution of y' = y − 6x such that y(2) = 2. Using a step size of 0.5, set y0 =…

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Q: Use the Adam-Bashforth method of the second order to solve the second equation y’=y(x+y) when h=0.1…

A: Given differential equation is y'=y(x+y), step size h=0.1 with initial condition y(0)=1 Let x0=0,…

Q: Use Euler’s method with n = 2 on the interval 2 ≤ t ≤ 3 to approximate the solution f(t) to y′ = t -…

A: Given, y'=t-2y y(2)=3

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: (B) Find the solution of f(z) = x'+6x°y+i 3x'y by using Cauchy-Riemann method %3D

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Q: Find the orthogonal trajectories of the family y = 1 - sec?r + C 4

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Q: A rocket travelling into orbit has a projectile given by the equation: f(x, y) = 3x3 + 2x² – 5x + 2…

A: As equation of projectile contain only x So y remain constant throughout the journey .Distance…

Q: 3. Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle…

A: given family of parabolas y2=cx at angle θ=60° claim- find the family of oblique trajectories that…

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: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Qe/ Salve the Euler- Cauchy equation xy'- xy+9y=o ?

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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: , obtain a formula for the local truncation error for the Euler method in terms of t and the exact…

A: Consider the given initial value problem y′=√(t+y), y(1)=3.

Q: : Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

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

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: x²y"+xy'-y= x 2

A: Given Cauchy-Euler equation is x2y''+xy'-y=x.

Q: 1. y' + 2y = x²y³ .2.3

A: Given problem:- solve the given differential equation y' +2y=x2 y3

Q: 8. Using the Runge-Kutta method of the fourth, solve y" = y + xy', y(0) = 1, y'(0) = 0 to find…

A: We take y'=z the Given equation is y''=y+xz,y(0)=1,y'(0)=0,y(0.2)=?…

Q: Find the extreme values of f(x, y) = x² + y² subject to the condition x²y = 1 using Lagrange…

A: solution is given below..

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

A: Power series solution of the differential equation

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 Cauchy-Euler equation: x*y' Зху + 4y = 0. %3D

A: Given Cauchy-Euler differential equation is

Q: (b) Find the general solution of: əz = yx² - xy Əx Given z = y when x = 1, determine the particular…

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Q: The orthogonal trajectories of y = ce5" where c is arbitrary constant. is - 2x + 2C = 5y? 2x + 2C =…

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

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Q: Find the maximum of f(x) = 4x – 1.8x2 + 1.2x³ – 0.3x4 using Newton's method %3D (xo = 3, ɛs = 1%).

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Q: Obtain the orthogonal trajectories of y=Cx^2 and compute for the positive value of y of the…

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Q: Q3/ Optimize the function Z = x + xị ? Subject to: x1 + x2 = 4 11,x2, 2 0 Using Lagrange…

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Q: Solve the follawing systen. 2 x, - 5x - cost dt dx2 b) by using the method of unde termined…

A: Given system is dx1dt=2x1-5x2-costdx2dt=x1-2x2+sint First, let us solve corresponding homogenous…

Q: Find the first approximation to the root of the equation x - 2x- 5 = 0using Regular-Falsi method…

A: Intermediate value property: Let f(x) be continuous function in a,band if f(a)>0, f(b)<0 then…

Q: Q3.lf f(x,y) = sin²(x-3y)+sin(xy find: 3 and aj ax Q4. Use Lagrange multipliers to find the shortest…

A: 3. If fx, y=sin2x-3y+sin-1xy   Find: ∂f∂x and ∂f∂y

Q: Find the orthogonal trajectories of the family of curves ey + 2x2 = k.

A: Given,  ey+2x2=k

Q: Use variation of parameters to obtain the general solution. y''+4y = 4 sec2x

A: The given differential equation is; y"+4y=4sec2x.

Q: Find the orthogonal trajectories of x2 + y? – 2cy = 0

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Q: 1 V1 – x z 1 – at x = 0 x, 2

A: Since you are asking part (c). We are answering only the (c) part for you.…