a) State the standard form for any third order linear homogeneous ODE with independent variable t and dependent variable x: b) What initial condition(s) are needed to make it a solvable IVP? State them in general form:

Q: Consider the ODE system x' = A et + 3 with A = 4 1 3 a) Use the method of diagonalization to find…

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: Let y1, y2,..., Yn be n linearly independent solutions of an nth order homogeneous ODE with constant…

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Q: Since Cov (X, Y) = E [X, Y] -E [X] E [Y]. Obtain Cov (Yi, BO)

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A: Here, one matrix function, A=1-223 is given Let the X=a1b1a2b2 So, X¯=AX=a1b1a2b2.1-223…

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Q: Q1. Verify Euler's theorem for the homogeneous funetion, fxy.2)-axy +byz + czu

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Q: Determine if the ODE is a homogeneous DE. If it is, state its degree. 1. у' 2ху2 yx2 +y3 -4/(x³y3)

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Q: Show that: (a) Cov(X,Y) = E[XY] – E[X]E[Y]. (b) If X and Y are independent, then fY|X(y|x) = fY(y)

A: Solution:a.Show that COV(X,Y)=E(XY)–E(X)E(Y)

Q: Let R = [0, 1] × [0, 1] . Est each with at least six rectan IR 6(x + y) dA 2

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

Q: DE : -t de dyx= 3et dt with indial conditins : xl0)=6 yl0)=1

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Q: Form a DE with respect to t: x = Acos (In t) + Bsin(In t).

A: Sol

Q: 비 az and Given that z = e*, x= 2u+ v, y= .y==. Find using the chain rule. au

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Q: Let P be the COM of a system of two weights with masses m1 and m2 separated by a distance d. Prove…

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Q: az Find if yz – In z = x + y ax

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Q: Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y||…

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Q: 6. Consider the ODE system below f = y? - ,2 = y +?. Which of the following is true? a. Solvable by…

A: Here we have given two differential equations. For a system of ODEs, we can use the elimination…

Q: In R', the point (1, 1, 1) does not belong to the cylinder x + y = 2. Select one: True O False

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Q: Let X and Y be independent and distributed as N(mu, 1). Is T=X-Y sufficient?

A: According to factorization theorem, if the likelihood function Lx,θ can be expressed in the form.…

Q: Consider, 21u = 2x – 3y and 21v = -–x+y Find the value of the Jacobian a (x, y) a (u, v)

A: 21 u = 2x - 3y, 21 v = -x + y

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Q: Let Uj, U2, Uz € R³ be an orthonormal system and let f : R³ → R be differentiable. Prove that af af…

A: Given that {u1,u2,u3} be an orthonormal system in ℝ3. Let us assume that {x,y,z} be the standard…

Q: Determine if the ODE is a homogeneous DE. If it is, state its degree.

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Q: Exercise 11.3 Prove the equality [* | f(x) dx = fm({x : [ f(x)| ≥ t}) dt, 0 where m is Lebesgue…

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Q: Which of the following DEs are first order linear DEs?

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Q: LZHP - DTNV. Complete the statement below. ZZ = _2_

A: Consider the following condition: LZHP~DTNV Hence, ∠L≅∠D∠Z≅∠T∠H≅∠N∠P≅∠V

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Q: An ODE is said to be stable if every abitrary constanst on its solution, such as C1 and C2 for…

A: Given  yh = C1*eat + C2ebt

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Q: To get a feel for higher order ODES, show that the given functions are solutions and form a basis on…

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Q: find c, and c2 so that y(x) = c, sin x+ c2 cos x will satisfy the given conditions. Determine…

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Q: Let {x; t = 1,2, ...} be a covariance stationary process and define y, = Cov(x, x+h) for h = 0.…

A: It is given that {xt: t = 1,2,…} is a covariate stationary process. It implies that, E(xt) and V(xt)…

Q: 59 An Analysis of antenna radiation patterns for a system with cir- cular aperture involves the…

A: Given equation is, gu=∫01frJ0urrdr Where, fr=1-r2 We know that ,Jnx=∑k=0∞-1kk!n+k+1!x2n+2k Thus…

Q: Show that the dyfferential equatian IS exact x(スt5in t) do + cast -2tu) abe +x² dt-

A: We will show that the given differential equation is exact.

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Q: that X and Y have joint pdf f(x, y) ={x + 3x^2y if 0 <= x <= 1 and 0 <= y <= 1, 0 otherwise.   (c)…

A: From the given information, Consider, the Joint pdf of X and Y is as follows: fx,y={x+3x2y if…

Q: Let y1, y2,..., Yn be n linearly independent solutions of an nth order homogeneous ODE with constant…

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Q: 2.) given this trigher ODE, use the reduction of HODE via of systems ODE and find the general non…

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Q: Show that lm Casy -1 CoSy-1

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Q: a- if w = f(u, v), u = x + y, v = x-y Prove that = ( - )* aw aw %3D ду du.

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