Given y1 (t) = t and y2(t) = t- satisfy the corresponding homogeneous equation of t'y" - 2y = - 3t – 2, t> 0 Then the general solution to the non-homogeneous equation can be written as y(t) = ciy1(t) + czy2(t) + Y(t). Use variation of parameters to find Y(t). Y(t) =

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A: Given diameter of sphere is d=30 units so radius of sphere r=d/2= 15 units

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Q: Use the mixed congruential method to generate a sequence of 32 random numbers with Xo=8, a=9, c=13,…

A: By mixed congruential  (µ) method Xn+1 = (aXn +  c) mod (m) Rn = Xn /32

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Q: Find the Laplace transform of: 1. f(t) = e(-4t)[sin(2t) – cos(2t)]² 2. f(t) = V1+ sin t + (6t)13 +…

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Q: 5s+3 6s 8 F(s) - (5s2+4s+1) s2+7 9.

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Q: Choose two figures which are topologically equivalent to each other 25

A: Solution :-

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Q: Describe the graph of the equation. r = -8i+ (1 – t² )j +t k O It is a parabola in the plane x = -8,…

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Q: Solve the eight eighth roots of z = -2 – j2/3. (express roots in polar form)

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Q: Choose two figures which are topologically equivalent to each other

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A: We can solve this using linear regression formula

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Q: Let f(z) = ((z – 3i)² + 9)ez- The Laurent series representation of f(z) in the domain 0 < |z – 3i| <…

A: Given function is fz=z−3i2+9e1z−3i. We have to find the Laurent's series representation of fz in the…

Q: Evaluate using Laplace Transform: tsin3 3t dt e-3t 00 f(t) ||

A: We have to apply the Laplace transform method.

Q: Find the Laplace transform of: 1. f(t) = e-3t) sin(2t) cos(3t) cosh(t)

A: Laplace transferom of the function

Q: 2. Is the graph below a tree? Why or why not?

A: To identify given graph is tree or not

Q: -2t y= c1e -1 1

A: For the solution of the problem follow the next step.

Q: Let G=Sg. 14 xy= 0 for XiyE 4G, would if X=0 or y=o hoppen! 4 true, prove it l4 true, prove it;…

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Q: Let R be the region shown in the accompanying figure. Fill in the missing limits of integration. y =…

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Q: 6. Let B be the region enclosed by z r +y and the plane z 9. (a) Compute the volume of B, using…

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Q: Choose two figures which are topologically equivalent to each other

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A: a. 10010two is converted into decimal form by expanding in powers as shown below.

Q: For each of the following series determine if the series converges or diverges. 00 In(n) n n=2 n3…

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Q: 1) A) Find the area of the portion of the sphere x? + y + =9 lying inside the cylinder x2 + y? = 3y.

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Q: The integral TT tan x sec2x dx O none of them is an impróper integral of type I that diverges is an…

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Q: 6. Interval, - TT <x < TT; function, f(x) = 0, = x2 - TT<x<T 0 <x< TT

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Q: Let S = (2x, 1 - x, x2 +x 1,x+ 1}. Then PA P1 O sis a basis for the nbove Sis a basis for the above…

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Q: Finel all the arymptotes of dhes cunue 4n" -13x2yay"+32yx2-3-20n²+74y2+16=0

A: Given equation is 4x4 -13x2 y2 +9y4 +32yx2 -42y3 -20x2 +74y2 +16=0 It can be written as 4x4 +9y4…

Q: f(t) = v1+ sin t + (6t)13 + t² sin 4t

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