Consider the following NLP problem: f(æ) = -x+ 2x1 – 122 – T2 +1 max s.t. I2 > 1. Determine if x = (,1) satisfy the first-order and second-order necessary %3D conditions.

Q: (b) Solve for the optimum to the following problem using the Karush-Kuhn Tucker conditions: Optimise…

A: Solve the following using the Karush-Kuhn Tucker conditions: Optimise fx1,x2=x1x2s.t.…

Q: Question 3 Consider the following NLP: max f(x1,x2) = -2x1 – a + 6x2 – 3x %3D 4x1 + x2 0 a) Obtain…

A: given max    fx1,x2=-2x1-x12+6x2-3x22s.t.     4x1+x2≤24               1          x1+2x2≤12…

Q: Question 3 a) Develop a first order method tor for approXivaating t' (x) which uses the data f…

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Q: All the following PDEs are nonlinear EXCEPT: (A) Uz 1 U₂ +-Uy= y U (C) Uaz + Uz Uy = 1 (B +u= F zy…

A: We find which of the given partial differential equations is linear.

Q: Solve the following problems а) ди ди = 1 + u, + 3x- dx t > 0, -o < x < ∞, dt u(x, 0) = f(x).

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Q: Consider the following initial-value problem i=x²-2r+t-1, 0≤t≤2, x(0) = 1. Use two steps of the…

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Q: what value of n can be used to transform the Bernoulli equation y'+p(x)y=q(x)y^n into an equation of…

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Q: 1) 3 Find the orthogonal trajectories of the family of curves y = 2x+k

A: Please see the explanation below

Q: 1. Answer the following questions: (a) Find the linear approximation of y- f(x)-Vr at a 256 and (b)…

A: Firstly, we will calculate f'(x), then f(a), f'(a).

Q: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0&lt;t&lt;2π)

Q: Solve the IvP y'+aty%3D1

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Q: Find the orthogonal trajectories of the given family of curves x - 4y c.

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Q: Consider the following problem: dT -a(T-T), where a=2*1012, at T(0)=4500, T,=200, find T(6), using…

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Q: the following constrained optimization problem using the method of Lagrange multipl max ln(xyz),…

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Q: Question 8 Z=8x+12y subject to 4x+6y214, 4x+5y29, x>0, y20 y=? (2 decimal places) Minimize

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Q: Find for following 1.y = (x + v3x)S

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

Q: Solve the following LP problem using the two-phase method max z= X1 +3x2 subject to X1+ x223 X1…

A: The given problem is Max Z =   x1 + 3 x2subject tox1 +  x2 ≥ 3x1 -  x2 ≥ 1x1 + 2 x2 ≤ 0and x1,x2≥0;…

Q: 2. Find the family of orthogonal trajectories of the given family of curves in the following…

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Q: In each of the following problems, find the Wronskian W(y1,y2)(x) of the given list of functions and…

A: By using determinant and derivative of functions we solve the given problem.

Q: An equation that considers both the above assumptions is dP P kP(1 M - dt

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Q: 1. Find the orthogonal trajectories of the family of curve a2+3y2 = cy ,where c is an arbitrary…

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Q: a) Find a function y whose graph passes through the point (1, -) and satisfies x²y' = y. b) Solve…

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Q: Find solution of an equation x X f(x) 1 1.0000 1.25 0.8000 1.50 0.6667 0.5714 1.75 2.0 0.5000 Using…

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Q: What are the control points of the splines Bezier curve from the two equations given below: a(x) =…

A: Given, ax=1+5x2+2x3...1bx=1-x+x3...2 The control points are lie on both the curves. So, to get…

Q: Part (c) Consider the initial value problem dy (t – 2)(t + 3) dt + (t – 5)y = tª + 1, y(-1) = 7.…

A: The given initial value problem is: (t-2)(t+3)dydt+(t-5)y=t4+1 ;       y(-1)=7

Q: PART B: Find the Orthogonal Trajectories of the given family of curves. 8. y = c²(x² + 4y²);

A: Given curve is: y4=c2x2+4y2 To find the orthogonal trajectories of the given family of curves. From…

Q: 2. Show that g(x)= *** has a unique fixed point in [0,1] and find an approximation to the point that…

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Q: Use your notes in 2 above to solve the following optimisation problem: Minimise f(x, y)=xy Subject…

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

Q: : Find the minimum of the following control problem: min f, (x? + 2xx + x²)dx If the endpoint…

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Q: Show that the Green's function for the Sturm-Liouville problem Ly = f(x) A1y(a) + B1y (a) = 0 A2y(b)…

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Q: 2: Find the orthogonal trajectories of xy=C.

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Q: Solve the following problem. (441)“ 2 max f = | (2x + u)dte dx 5 – u?, x(0) = 1, x(2) free“ dt %3D -…

A: We will use the basics of integration theory to answer this question.

Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

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Q: 1. Find the orthogonal trajectories of the family of curve a+3y2 = cy ,where c is an arbitrary…

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Q: Find the first three iterates appling successive approximation for the initial yule problem x² = x x…

A: Given that x'=x, x0=1

Q: nake/s the DE nonlinear y' =1-xy+ y2

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Q: if the implicit function is x3=at2, find the d2x/dt2

A: if the implicit function is x3=at2, find the d2x/dt2

Q: Solve the given problem Homogeneous y5 + x5 y' = x³y2 on Functions.

A: Given homogeneous differential equation isy'=y5+x5x3y2

Q: compute the first three successive approximations to the solution of the ini- tial value problem dx…

A: Given: dxdy=2x-yand x0=1 We have to find the first three successive approximations for the given…

Q: . Classify the following PDE as (i) Linear or Nonlinear, (ii) Homogeneous or nonhomogen eous a ru -V…

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Q: Verify that the function y(r) = 2, is a solution of the initial value problem dy + 2y = 3y, v(0) =;…

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Q: The solution of the nonhomogeneous DE y" + 4y' +4=5e* is

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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: Solve the following optimization problem by using Lagrange method: Maximize f(x,x;)=2x, + x, – 3x²…

A: Lagrange Multiplier Method:- This method is used to optimize a function on a region that contained…

Q: For the family x² + 3y2 = c, find that member of the orthogonal trajectories which passes through…

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Q: Consider the following initial value problem: dy = -ty + dt 4t y(0) = = 1. Use the midpoint method…

A: The differential equation given is as follows: dydt=-ty+4ty Where ft, y=-ty+4ty. With the initial…

Q: Find the general solution to 3 1 0 0 3 1X. -X= dt 0 2

A: We first find eigen values, then corresponding eigen vector to solve the given system as in next…

Q: Consider the following blending problem, where the gredient x3 is a semi-continuous variable: min…

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Q: QUESTION 7 f(x) = 3 x4-4 x3 -12 x2 +1, has local minimum at x= %3D O A O B 2- ODO

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