Find the autocorrelation function, R(t) of the following Gaussian function: z1) = (). exp 2TO 202 The following identity might be useful: | r(t)dt = 1.

Q: (a) express dw/ dt as a function of t, both by using the Chain Rule and by expressing w in terms of…

A: Given- w=x2+y2, x=cost, y=sint and t=π To Find- The value of dwdt as a function of t, both by using…

Q: Solve the IVP using Laplace transforms. x'(t) = t?, x(0) = 4

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Q: Transform the following Bernoulli differential equation of the form 2+ P(x) · y = dx Q(x)y" or +…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: b) Use Laplace transform to solve the system of differential equations UTM dr UTM x = 4y, dt y+Bet…

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Q: Consider the function z=x ln(1+ y“), if x=2-t and y=\t , use an appropriate form dz of the chain…

A: According to the given information, consider the given function z.

Q: Which of the following represents the derivative of t cos(t) dt? 1-5x 0. gʻ(x) = (1 – 5x) cos(1 –…

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Q: Solve the solution of the DE of the Gompertz function: dP = c ln| dt In[P

A: To solve the given Differential Equations.

Q: The equation implicitly defines as a function of t. Find dr dt da dt 11 2 cos (6 x) = -8

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Q: (a) express dw/ dt as a function of t, both by usingthe Chain Rule and by expressing w in terms of t…

A: Consider the following equation: w=x2+y2 Substitute x=cost+sint and y=cost-sint in the above…

Q: 2(3) Calculate the following commutators: (a) [d/dx, x·d/dx] (b) [sin(x), cos(x)] (c) [x^2, Ĥ] ,…

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Q: Solve the following equations by Laplace transforms. dx (a) +3x =e-2t given that x = 2 when t = 0 dt

A: Since every part is independent of each other so according to the guideline , I am going to solve…

Q: Let z be defined implicitly as a function of x and y by the e e-zy əz find O UTM + cos (xy) = (4 –…

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Q: (a) express dw/ dt as a function of t, both by usingthe Chain Rule and by expressing w in terms of t…

A: A) The function x is differentiated as, x=cost⇒dxdt=-sint The function y is differentiated as,…

Q: 7-10 Use an appropriate form of the chain rule to find dw/dt. w = 5 cos xy - sin xz; x = 1/t, y = t,…

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Q: 1. Consider the function z = x In(1+ y²), if x 2-t and y= Vf, use an appropriate form %3D dz at t…

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Q: Find for x = x(t) defined implicitly by 25+25 x In(t) = e25xt Also evaluate dt at (t, x) = (1,1).

A: Given,25 + 25xlnt = e25xtTaking 'log' with base 'e' on both side, we getln25 + 25xlnt = lne25xtln25…

Q: Use the Laplace transform to solve the given system of differential equations. dx = 3y + et dt dy =…

A: We have given two equations dxdt=3y+et                ...(1) dydt=12x-t                ...(2) The…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: See the detailed solution below.

Q: (a) express dw/ dt as a function of t, both by usingthe Chain Rule and by expressing w in terms of t…

A: (a) Consider the provided equations, w=2yex-lnz, x=lnt2+1,y=tan-1t  and z=et ; t=1  Express dwdtas a…

Q: (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

A: We find dw/dt using chain rule. Here plug x = cos t, y = sin t, z = 4sqrt(t) and simplify.

Q: Suppose P is a linear differential operator that factors but has variable coefficients. Do the…

A: If P is linear  differential operator that factors but has variable coefficients ,

Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

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Q: Determine if the following functions are linearly dependent or independent by determining their…

A: The Wronskian of a set of function y1, y2, y3 is defined as, If the Wronskian W is non-zero then…

Q: The expanded form of the differential operator D(xD - 1) is (A) XD²-1 (в XD²+1 XD² - D XD² D

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Q: Solve the following equations by Laplace transforms. dx - dt + 3x = e-2t given that x = 2 when t 0

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Q: Consider a regularizing term defined by where k!2* and the linear differential operator D is defined…

A: We are given the following regularizing term.                    ∫ℝN0DF(x)2 dx=∑k=0∞ak∫ℝN0DkF(x)2 dx…

Q: Consider the following. w = cos(x - y), x - t2, y = 59 (a) Find dw/dt by using the appropriate Chain…

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Q: 10. Show that the function f(x, y, z) = e³x+4y cos 5z satisfies the Laplace equation.

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Q: д. L. = a(x, y)+b(x, y) +c(x, y). – d(x, y) -

A: Proof: Consider V be any vector space of all functions of two variable x  and y whose partial…

Q: The differential operator (D2 - 16D+113)³ annihilates the functions

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Q: Use Laplace Transform to solve the following initial- value problem: (2) dx + xy 4x y(0) = 0, ỳ(0) =…

A: Given, dydx+xy=4x , y(0)=0 ,y'(0)=2 Taking Laplace Tranform throughout the given Differential…

Q: 1. -ay + A sin dy 2 = Br, dt

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Q: Consider the following. d²x = t² dt² d²x - = 6t dt² x(0) = 4, x'(0) = 0, y(0) = 0, y'(0) = 0 Give…

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Q: Find a linear differential operator that annihilate the given function a) y=7e2x b) y=x+3xe6x

A: We know that gD is annihilator of y if gDy=0 (a) y=7e2x Differentiating wrt x, Dy=7×2e2x, D=ddx is…

Q: (a) express dw/ dt as a function of 1, both by using the Chain Rule and by expressing w in terms of…

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Q: Show that the p.d.f. of Z is given by g1(r) = e-1(+A)cosh(vAx), x > 0, where cosh(2) = }(e² +e=*) is…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: 3. Use chain rule to find given w = Vx2 +2y2 + z² and a cos (st), y = -2s In t ane 2 = 3s?Vt. 3s2Vt.

A: Follow the procedure given below.

Q: If C, and C, are constant vectors and A is a constant scalar, show that H - e* (C1 sin Ày +C2 cos…

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Q: Using the second fundamental theorem of calculus and chain rule, compute t dt. t+1 dx 2x

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Q: y" + 4y' + 3y = 1– Uz – U4 + Ug , -

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Q: Use the Laplace transform to solve the given system of differential equations. dx = x - 2y dt dy 5х…

A: Hey there. Since you have sent more than one question we are bound to do just one question at a time…

Q: Use Laplace transforms to solve the initial value problem x"'+x = cos3t; x(0)= 1, x'(0)=0

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Q: 1-t2 The differential of u=In, is 1+t?

A: Given u=ln1-t21+t2

Q: Use the Laplace transform to solve the given system of differential equations. dx/dt = -x+y dy/dt…

A: Given: A 0.25 kg object with the speed of 6 m/s at point A and kinetic energy of 8 J at point B.

Q: 1- Find dwi dt at the given value for w ==+2,x = cos (1), y = sin (1),z = w =-+ at = 3

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Q: Suppose w=x/y+y/z, where x=e^(4t), y=2+sin⁡(4t), and z=2+cos⁡(3t). A ) Use the chain rule to find…

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Q: Solve the following differential equation using the Laplace transform dy 4- dt + 6y = 3t if t = 0…

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Q: 1. On (–1,1), two functions Y1 (x) = e2« cos x, y2(x) = e2ª sin x are linearly independent linearly…

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

Q: Q1) Suppose w =÷+ ?, x = cos² t, y = sin² t, z = ; Evaluate dw at t = 3, by using the Chain Rule dt

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.