show Itat the differential equation メり dy - -2-ye" dx xーとリ Xe 29 its exact and find its Folution

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A: We have to find the general solution of given heat equation.

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Q: Use the quotient rule to find the derivative of the following x - 9x + 5 y= X +7

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Q: 11. Find all zeros of the polynomial P(x) = 2x + 7x + 5x³ + 7x?+ 3x. %3D

A: This we shall do by inspection method. The detailed solution typeset in latex is presented as the…

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A: Error of trapezoidal rule  Er≤b-a12h2M Where M is maximum value of f''x

Q: Use X = eAtC to find the general solution of the given system. %3D 0 0 0 X' =5 0 0X 7 10 X(t) = %3D

A: We will find eigen values and corresponding eigen vectors  of the equation to get general solution

Q: Obtain the following Laplace ti 1) L{cos3t + 5e-t} 2) L{e¬3t (2t² – 5t + 1)} 3) L{sin7t – cosh3t} -

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Q: x y z Find the value of 35 25 45 if it is known that y u v w = -9. u V w -7 -5 -9

A: Obtain the equation by solving the given determinant then use it to obtain the determinant of the…

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Q: In Exercises 1 and 2, we consider the system dx 2x + 2y %3D dt dy = x + 3y. dt For the given…

A: Disclaimer: Since you have asked multiple question, we will solve the first question (Ex 1) for you.…

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A: To explain: What will be the result when we apply Gram-Schmidt process to a linearly dependent set…

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Q: 16. Find the solution of the wave equation for the vibrating string that satisfies the initial…

A: See answer below.

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Q: v= 8 x° + 28 x* – 34 x° – 83 x² – 46 x – 8 6x³ – 19 x* – 22 x³ + 52 x² + 64 x + 15 10. x2 + 2x +1

A: To Sketch: (9) y=8x5+28x4-34x3-83x2-46x-8 (10) y=6x5-19x4-22x3+52x2+64x+15x2+2x+1. And To mention:…

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A: By the Alternating series Remainder theorem we have |S-Sn|&lt;RN&lt;=bN+1.

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A: We have to express the given function f(t) as a Fourier series expansion.

Q: 2. Consider the two systems of differential equations da dx (i) = 0.3x – 0.1xy (ii) = 0.3x - 3xy dt…

A: Given system of differential equations: (i). dxdt=0.3x-0.1xydydt=-0.1y+2xy (ii).…

Q: 9 what is the Max and min ¿ (4) att ained by f (t)? values (S)oea of oerb le o ) Sketch the graph of…

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Q: , Prove that if A is an all-zero matrix for some k > 1, then 0 is the only eigenvalue of A.

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Q: 8:3 18. Coeficient of correlation between two points. From the followiag given sets of observations…

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Q: Q2: A: Find the maximum for the function y = (1+ e*) sinx near x=2.5. Use Quasi-Newton method with…

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A: When using a conventional normal distribution (also known as a Gaussian distribution): Approximately…

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A: Solution :-

Q: OSenies exponsion exponsio (2-0)(2-2) 1< |2 - 5| <3

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Q: Let A be an m x n matrix over R. We define NA := {x € R" : Ax = 0}. NA is called the kernel of A and…

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Q: Using the Alternating Series Remainder Theorem, determine the number of terms N required to…

A: Error estimation theorem is used

Q: Problem 1 Find the phase difference between leading. I = 2 cos (wt+10°) V = 3 sin (wt-10º) (i)

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Q: 2) Explain the definition of linear independence/dependence of n functions fi(x), f2(x),..., fn (x)…

A: The given functions are f1x,f2x,...,fnx and also the sine functions are sinx, six2x, sin3x. To…

Q: Use X = X + X, = eAtC + eAt * e-As F(s) ds to find the general solution of the given system. x- (:…

A: We can solve this using given information

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Q: 2. Solve the following homogenous differential equation dy 2ry = (a + 3y). |3D

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Q: False. Provide a counterexample if a statement is False. subset of R3. 1. True False If V xF =0 in…

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