Solve the initial value problem using a power series. y" + 1xy' - 4y = 0, y(0) = 9, y'(0) = 0. [Hint: give the answer as a polynomial of degree 4.] Y

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Q: Q: Let T: R² → R² be given by T(x, y) = (x, −y). Then show that T is a linear operator.

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Q: Verify the initial value theorem of f(t) = 1 +e¯t[sint + cos os t]. 3 1 0 2

A: Solution :- As per guidelines I solve only first question .

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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: Use the binomial series to expand the function f(x) = and state the radius of convergence. (1+x)4 as…

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Q: Find the solution to the following differential equations 1. (D^2 +1) y = tanx 2. (D^4-1) = 0

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Q: Solve the differential equation by variation of parameters. y" + 2y + y = e-t In(t). -t 2e t²ln t…

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Q: Find the general solution of the system of equations 8 -4 t x': (₁ 1 ) x + ( ++ ³2₂) ₁ ² > t> 0. 16…

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Q: 8. Use the method of Laplace transform to solve the initial value problem y" - 2ay' + a²y = (a - 3)²…

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Q: 2. The slope of the surface = ry² in the r-direction at the point (2,3) is. slope of this surface in…

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Q: Let D = {0,1,c,d} be an integral domain. Explain why the following are true: (1) If 4.1=0 then 2.1 =…

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Q: The line given by -6x - 4y = -8 is dilated by a scale factor of k = 5, centered at the origin. What…

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Q: Find the eigenvalues and eigenfunctions. 26. y" + Ay = 0, y (0) = 0, y' (π) = (

A: Given boundary value problem is y'' + λy = 0 ,   y(0) = 0, y'(π) = 0

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Q: 7. Find the truth value of the following biimplication a. ²log 16 = 4 if and only 24 = 16

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Q: Find the laplace transform of f(t) =1/4 e^2t sin(2t)

A: Find the laplace transform of f(t) =1/4 e^2t sin(2t)

Q: · Let F(x) = sin(4t²) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.69 Use this…

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Q: Use the Laplace transform to solve the given system of differential e dx 4x + d³y dt3 = 12 sin(t) dt…

A: dxdt−4x+d3ydt3=12sintdxdt+2x−2d3ydt3=0x0=0, y0=0, y'0=0, y''0=0

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Q: In Exercises 1-4, apply the Jacobi method to the given system of linear equations, using the initial…

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Q: Determine the multiplicative inverse of 11 in Z24. Your final answer should be an element of (0, 1,…

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Q: Find the laplace transform of ?(?) = sin(2?) cos(2?)

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