3 , 04' a.) Rewrite f (t) in terms of the Unit Step Function, U (t – 4). b.) Find F(s)=L{f(t)}

Q: 4. z = tan-'(y/x), x = e', y = 1 - et

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Q: A. From the Laplace table, determine F(s). 8. f(t) = te-2t cos 3t

A: Given that: f(t)=te-2tcos3t

Q: function u (t) == C, cos(@ot – ao) that would result if the mass on the spring were set in motion…

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Q: Use the chain rule for one independent variable Question Let w(x, y, z) = xy cos(z), where x = t, y…

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Q: Obtain an asymptotic expansion for I(z) = S e-zy°/2 cos y? dy, along [0, 0). as z → 00 -00

A: As per the question we have to find an asymptotic expression for the integral I(z). And we will do…

Q: þ/ Show that the function satisfy Laplace equation f(x,y) = In /9xy+3y² Q/ find by using chain rule…

A: Since you have posted multiple questions ,we solved the one question for you  To get the solution of…

Q: The acceleration of a particle moving back and forth on a lineis a = d2s/dt2 = π2 cos pt m/sec2 for…

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Q: Use the Chain Rule to find dw/dt. + y2 + z2 x = 5 sin(t), y = 7 cos(t), z = 6 tan(t) W = In

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Q: Q2) A) Verify that wxy wyx for w x sin y+y sin x +xy. %3D R) Show that f(x v) = e-2y cos 2r…

A: See the details solution in below

Q: Show that the function z = arctan y/x satisfies Laplace’s equation                           ∂2z/…

A: Consider the following equation:

Q: T 2 If fo)= J* +?dt, use the fundemental theorem of culculus part 1, to find f'cx) fixs=

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Q: e moves along line segments from the origin to th F(x, y, z)=z²1+ 3xyj + 2y²k. work done.

A: In this question, the concept of line integral is applied. Line Integral The function to be…

Q: What is laplace y(s)=(s^2+2s)/s^4,find y (1)?

A: Use laplace inverse

Q: The work done W,to stretch a spring from its natural length to an extension of b meters Is 6. given…

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Q: Q1- The divergence of the function f = (r5 cos 0)e, in spherical coordinates is...

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Q: What is the laplace of L(f"(t))? A s2F (s) – sf (0) – f (0) B sF (s) - f(0) Osf (0) - f(0) D s2F(s)…

A: as per our company guideline we are supposed to answer only one question. kindly post remaining qs…

Q: Solve the equation using Laplace transforms. y' – 5y = 8(t), y(0) = 6. Evaluate your soltion at t =…

A: we are given , y'-5y=δ(t) taking laplace  L(y') - 5L(y) = L[δ(t)] from laplace table we are using ,…

Q: f(x, y) =(e-2y)Cos2x

A: The Laplace equation is: ∂2f∂x2+∂2f∂y2=0

Q: The linear approximation at z = 0 to sin(4z) is A+ Bz where A is: and where B is:

A: Linear approximation is found by L(x)=f(x)+f'(x)(x-a) Differentiate L(x) with respect to x.…

Q: A force of F = 14x – x N stretches a nonlinear spring by x meters. What work (in J) is required to…

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Q: Let w(x, y, z) = x² + y? + z? where x = sin( – 7t) , y = cos( – 8t) , z : dw by first finding dt dx…

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Q: Given D = e* sin y ax – e¯* cos y ay. Find divergence of D. -

A: Calculate divergence: div. ∆=∂∂xe-xsiny+∂∂x-e-xcosy         =-e-xsiny+e-xsiny         =0

Q: Encontrar la transformada de laplace de la función f(t) = { 2, si 0 2π

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Q: Show that the function satisfies the Laplace equation f (x, y, z) = (/x2 – 2y² + z?)*

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Q: a. Express the function f(t)=- its Laplace transforms. π-t, sin t, 0 π 15 terms of unit step…

A: Introduction: The unit step function is a significant special function. It is a piece wise constant…

Q: Use the Chain Rule to find dw/dt. w = In Vx2 + y2 + z2 ), x = 4 sin(t), y = 6 cos(t), z = 5 tan(t)…

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Q: 1) f(t) =t cos(@t) 2) f(t)=tsin(@t) 3) f(t) =t cosh(at)

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Q: Find r'(t) and intergral of r(t) dt, where r(t)= t sin(t)i +sin2(t) cos (t)j + 3/ (1-t2)1/2 k.

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Q: If z = x? + y?; x = t sin t , y = 2t cos t dz then dt at t = is

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Q: .a. Compute the divergence of the function (V. v) v = (r? cos?0) î + (r² sin²e)ð + (r sin® cosø)

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Q: 4y The divergence of the vector G = i+ sin y j+ 3k is :- -8y + cosy x3 الخيار 2 O

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Q: Assume that a body moving with velocity v encounters resistance of the form dv/dt = -kv3/2. Show…

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Q: Let f = (r +2ryz)i+( + 2xy)j+ (+ 2xyz)k. Find j at (1.0, 1). (a) divergence of

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Q: Q2) A) Verify that wry wyx for w x sin y +y sin x + xy. %3D B) Show that f(x, y) = e-2y cos 2x…

A: A) given that w=x siny+ y sinx+xy               ...i show that- wxy=wyx differentiate equation (i)…

Q: What is the laplace of L(f"(t))? A SF (s) f(0) (в B s2F (s) – sf (0) - f'(0) © s2F(s) - sf (0) -…

A: Use the definition of laplace transformer and derive the required solution.

Q: 3 find the invers laplace f(t) = S+3 s²+3

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Q: Q1- The divergence of the function f = (r5 cos 0)e, in spherical coordinates is.. .

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Q: Q1- The divergence of the function f (r5 cos 0)e, in spherical coordinates is...

A: The given problem is to find the divergence of the vector function in spherical coordinates.

Q: Q2) A) Verify that wry Wyx for w x sin y +y sin x + xy. s) %3D B) Show that f(x, y) = e-y cos 2x…

A: We have to verify that the equations satisfy the given conditions.

Q: Assume that w= f(s° +t*) and f'(x) = e*. Find and dt D I3D 次咖一。

A: Finding the expression of w and proceed the differentiation

Q: Using an appropriate linearization, the local linear approximation of f(z)= T+ sin z at 27 is

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Q: Assume that z and y are both differentiable functions of t and are related by the equation y = cos…

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Q: Use the Chain Rule to find dw/dt. w = In( V x2 + y² + z? ), x = 2 sin(t), y = 7 cos(t), z = 8 tan(t)

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Q: Show that f(x, y) = ea# (A cos(ay) + B sin(ay)) satisfies Laplace's equation: + - 0. dy?

A: Given,            f(x,y) = eαx(Acos(αy) + Bsin(αy))             Then show that  ∂2f∂x2+∂2f∂y2=0

Q: fi at nd laplace: {e}

A: Use the formula for the Laplace Transform for the given function.

Q: Q2) A) Verify that wxy = Wyx for w = x sin y + y sin x+ xy. B) Show that f(x, y) = e-y cos 2x…

A: Here we have to find the partial derivative of the functions with respect to x and y seperately…

Q: (c) Show that the function z = e* sin y + e cos x satisfies Laplace equation azz azz = 0. ax? ay?

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Q: 2xy Show that f (x, y) = tan satisfies the Laplace x² – y? Equation f + f, =0 XX yy

A: We have fx,y=tan-12xyx2-y2 We need to prove that fxx+fyy=0 Now,  fxx means derivative of f with…

Q: Evaluate the inverse laplace fo 1-7 (s-2) (s+2) णुन तिथ ( for Partial fractiens and verify you:…

A: Given that, L-11s-2s+22

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.