Solve the equation .11 y" + 3y' + 2y = x2

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A: The solution is given as

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A: Properties of the exponent lnab=lna+lnblnab=lna-lnblnab=blna

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Q: x dx

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Q: Problem 22.8 Solve by Laplace transform Utt - 9urr = 0, 0 0 u(0, t) = u(T, t) = 0, %3D u (x,0) = 0,…

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Q: 1- Show that the following subset is a subgroup. H = {0 e S, l0(n) = n}c S,

A: We have ,  H = σ ∈ Sn / σn = n  Here , H is subset of Sn Clearly , identity permutation is in  H.…

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Q: Suppose A is a 2 x 2 matrix such that for all x, y E R², (Ax) · (Ay) = x ·y Must it be true that A…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

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A: We have used the iteration formula of Newton's method.

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Q: 3. (a) Determine the value of coefficient a for which the vector field F = (ayz + 22, 2.02?, 6ryz² +…

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Q: 2- 3x | 1/3 s xs 2/3 3x - 2|2/3 sxs1} (a) Sketch a graph of R(x). (b) Find all fixed points of R (c)…

A: This is a problem of a real-valued function.

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Q: Suppose w =+ , x= cos? t, y = sin? t, z = = }; dw at t = 3, by using the Chain Rule dt Evaluate

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Q: please send step by step handwritten solution Q1

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Q: Use the fact that dim(R(A)) = dim(C(A)) to explain why rank(A) = rank(A").

A: Here we can use the fact that  rankA=dimRA to prove the identity.

Q: 1 (a) Find the expression for Vo given that ø(x, y, z) = r=3, where r² = a² +y²+z².

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A: Take R = Z[i√5]  Clearly, R is commutative ring and Z ⊆ R  Also, 2,3 ∈ R are not prime but…

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A: See answer below

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Q: Problem 22.8 Solve by Laplace transform Uu - 9urr = 0, 0 0 u(0, t) = u(T, t) = 0, %3D u (x,0) = 0,…

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A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…