Consider the following problem; max f(x1 ,x2) = -x? – x3 subject to (x1 – 1)³ > x3 d. Try to find the max through FoC of Lagrange.

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: Find the local minima, the local maxima, and the inflection points of

A: Given,            A(x)=∫3x t dtt2+1

Q: An insect is in a toxic environment. The level of toxicity is given by T(x,y)= 2x* – 4y° If the…

A: Tx=0⇒x=0Ty=0⇒y=0Using D-TestD=TxxTyy-[Txy2]D=0 at (0,0)   T(x,y) is minimum

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: Obtain the particular solutions of the following: (y-Vr² + y² \dx– xdy =0, y(0)=1 a.

A: Solution is given below:

Q: In the given question , find d2y /dx2 implicitly in terms of x and y :-   xy - 1 = 2x + y2

A: In the given question , find d2y /dx2 implicitly in terms of x and y :- xy - 1 = 2x + y2

Q: Suppose a person wants to travel D miles at a constant speed of (30 + x) mi/hr, where x could be…

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Q: +] has the general solution u(x, y) = e"[f(x)+g(y)] where f and g g are arbitrary functions

A: ∂2U∂xdy+∂u∂x=0let U(H.Y)=e-yf(x)+g(y)

Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: b. The maximum deflection of a beam occurs at x satisfying 2x? – 3Lx + L? = 0 Where L is the length…

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Q: 5. Show that 1 T = VI? + y? satisfies the equation Tz + Tyy = T3

A: Given T(x,y)=1x2+y2

Q: Employ Picard's method to obtain y (0-1) of the equation y,=0 when x =0. :=x² +y}, given that %3D

A: Given IVP is dydx=x2+y2, y0=0 when x0=0 Let f(x,y)=x2+y2 , y0=0 when x0=0. Formula for Picard…

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: Given f(X)=−xe^x whats the root of the linearization of f(x) at a = 4.3?

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Q: Find the 2nd solution using reduction of order. t²y" - 4ty +6y=0;t> 0; y₁=t²

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Q: f (x) = 5.6 sin (2.6x – 4.2) – 9.1- What is the equation of the midline of the function %3D o y =…

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Q: Solve the following problems by the method of undetermined coefficier 1. (D² – 4D – 5)y = x² – 2x +…

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Q: - Employ Picard's method to obtain y (0-1) of the equation ay = x +y, given that Y, =0 when x, = 0.

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Q: Solve using variation of parameters or reduction of order (D² – 3D + 2)y = (1+e²x)¯2

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Q: Solve the non-homo. D.E. 1.y" + у%3D Зе2x

A: Differential

Q: ľ Solve the following optimization problem (using second order conditions to confirm your…

A: note :  As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: e. Find points on the graph of xy°z² = 16 that are closest to the origin.

A: Let P be point (x0,y0,z0) Then, distance between P and origin is given by

Q: Solve the following Euler-Cauchy type equation: 1 (x² D² + 3xD+ 1)y = - 3xD+ 1)y = (1 – x)² ' d…

A: Given equation is, x2D2+3xD+1y=1(1-x)2 Take, (x2D2+3xD+1)y=0 Then assume, y=xn,…

Q: Find the general solution of the equation xy' = ky that is valid for x > 0.

A: We have to find y(x) for this equation which is valid for x>0. We use integration to solve this…

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: sing the method of variation of parameters to e a nonhomogeneous DE with = -ex, W2 = e W2 = e-1Ix…

A: Wronskian of the function

Q: Suppose that z = 3 – i is a root of the equation - ax" + bx + cx + d = 0, a,b, c, d E R

A: given one root of the equation ax7+bx4+cx+d=0. a,b,c,d∈R is z= 3-i we know that complex roots occurs…

Q: 1. Solve for the othogonal trasctories y =x²(1-cx)

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Q: у" — у' — х %3D 0

A: We are given: y'''-y'-x=0⇒y'''-y'=x Auxiliary equation is : m3-m=0⇒m(m2-1)=0⇒m=0, 1, -1 Hence,  CF=…

Q: | (3x+-x²) dx=Ax° + Bx² +C, for Suppose that %3D constants A, B, C. What is the value of C if the…

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Q: Find the general solution of the following ODOS: (а) x2y"-Зху'+4у3D0, х>0.

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Q: A rectangular plate with an area of 36 cm? is to be produced on a lathe in such a way that the…

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Q: The graph of y=x'-3x-24x +32 is concave upward on the interval (1, oo) because: O'=y"=0 Oy' is…

A: The given function is y=x3-3x2-24x+32

Q: - Use Euler's method to estimate y(3) given y(0) = 1, and y' = x -. Use steps of h = 1

A: use euler method for finding the y(3)

Q: dy + ydx %3D = 3x²y?dx,

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Q: Find the maximum of the following equation f(x) = -4 x³ +3 x² + 25x + 6 By using newton's method,…

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Q: The function f(x, y) = -2x² + 4y² - 12 has a local maximum at the point (0,0). Select one: O True…

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Q: Q2:-Using Newton-Raphson method to find root of f(x) = 2e* –1, xo = 1 %3D

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Q: Determine a particular solution of the following using the method of variation of parameter. TH…

A: Here we first find the auxiliary equation. Then we can find out the complementary function, in…

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: Apply the appropriate method to solve the Cauchy-Euler equation 2x²y "+ 5xy'+ y = x² – x

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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: Find the roots of the given equation where f(x) = 0 with the stopping criterion of 0.001. f(x) = (x…

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

Q: 1o9.. 10 11 12 What is the minimum value of y = -3 – 5 sin (4x)?

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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: Solve the non-homo . D.E. 1.y" + у %3D Зе2х

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Q: At what x-value(s) on the interval [-2, 3] does the graph of f (x) = x² + 2x – 1 satisfy the M.V.T.?

A: According to mean value theorem,Let f be continuous on [a,b] anddifferentiable on (a,b). Then…

Q: 25 p1 3) Compute f(x)f'(x) dx where f(x) =x +2, using the Composite Trapezoidal 2 rule, your results…

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

A: