By using the unlimited coefficients method, choose the correct answer for this equation y"-3y"+3y'-y=sin(x) : Yc = (C₁ + C₂x + C3 x³)e²x Option 1 Yc = (C₁+C₂x + С3 x²)e-³3x Option 2 Ye= (C₁+C₂x + С3 x²) e ³x

Q: Solve the system 7 -1 [7] 6 2 dx dt with the initial value -6 -A [[:] x(0) = -15 x(t): || X

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Q: Solve e^(3z-7)=1

A: Given,  e3z-7=1 ⇒lne3z-7=ln1   [Taking logarithm both sides] ⇒3z-7=0   [since lnea=a   and   ln1=0]…

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Q: . Consider the vectors W₁ = W2 1 0 and the subspace W = span{W₁, W2, W3} CR¹. (a) Find an orthogonal…

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Q: (*) Find the Fourier cosine series of f(x) = sin(4x) on [0, π]. Could you guess what the Fourier…

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Q: Q: Find A least-sayvares solutions of Ax=b 1 -2 3 - 1 2 O d 3 ", 5 : دا 1 -4

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Q: Item 1: Derive the following: Table 1: Addition Table for Zg Table 2: Multiplication Table for Zg…

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Q: Use bisection method to find the root of x^3 –x^2 – 3x – 3 with two initial points xl=3 and xr=2 and…

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Q: Consider the convolution f(t) = 26 U (t-18) where U corresponds to the * step or heavyside function…

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Q: Find the differential equation such that y(x) = c₁(x-4)³ + c₂! 64x² d²y + +60x+y=0 dx² dx 64(x-4)²…

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Q: Interest (Php) Matu

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Q: Taylor Series Approximation Formula f" f"" (a) ² f(x) = f(a) + f'(a)(x − a) + ¹¹¹(a) (x − a)² +…

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Q: 6. In the process of calculating given by: s-1 al + -84-1 - 1)² + a² Determine the value of B² {o…

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Q: mod can be applied if the function is continuous only.

A: We have to check whether the Fibonacci method is applied if the function is continuous only.

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Q: Evaluate the integral by completing the square and using trigonometric substitution. dx s √5 + x −…

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Q: 3. Considere la función e-2 sit > 5 f(t) = 2t si 0≤ t ≤ 5 To calculate {f(t)} using the definition,…

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Q: Suppose that Y₁(t), Y₂(t), and Y₂(t) are solutions of the differential equation y"+5y"+(2-t)y=0.…

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Q: Let u = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that u + v and w are…

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Q: 3. Answer the following questions. Show all solution steps: x3 y6 z4 a. Simplify: ÷ 2(x4y7)⁰ xm y2…

A: (a) we have to simplify x2x4y70÷x3y6z4xmy2z-5 also, m=2 Then x2x4y70÷x3y6z4x2y2z-5

Q: Find the arc length of r(t) = 3 cos ti + 3 sin tj + 5t^(7/2) k

A: The given vector is r→t=3 cost i^+3 sint j^+5t72 k^....(1) To find: the arc length of the vector.

Q: Find the differential equation such that y(x) = c₁(x-4)³ + c₂! 64x² d²y + +60x+y=0 dx² dx 64(x-4)²…

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Q: Consider the linear system dt = AY with A = Find the corresponding straight-line solutions Y₁ (t) =…

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Q: 24 Across:  The ___________ of a BVP quite often are proportional to the natural frequencies of the…

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Q: Use substitution to find the general solution of the system x₁ = 3x₁ + 7x2, x2 = 3x1 - 1x2.

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Q: Scenario 2: The mean content of 25 bottles of brand S mango juice is 255 ml with a standard…

A: Given : μ = 360 ml Ẍ (Mean) = 355 ml σ (Population Standard Deviation)= 9 ml α= 0.01

Q: Provide an example of a topological space that is connected but not path-connected,why?

A: We use definition of connected and path connected sets. We use contradiction method.

Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution:f:[a,b]→ℝ is differentiable at x0(a,b)Let us take upper derivative at x0+then…

Q: 2- Let f: [-2,2] → R be defined on [0.2] by f(x)= {2 prove that f is Riemann integral. X≤0 x < 0

A: Given : f : [-2, 2] →ℝ defined as   f(x) = 3x≤02x&gt;0. To prove : f is Riemann integrable.

Q: 1.2. In the process of calculating L-¹ given by: -2.L -2s +3 we get an equivalent expression 10s 7 ^…

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Q: Suppose that a numerical method is used to approximate the solution of an initial -value problem…

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Q: o q Lor -00 10 The function determining the shapes above is f(x) = a√z. The area shown on the first…

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Q: 4. Solve the following initial value problems: (a) y" + 5y' +6y=e-'8(t-2), x' - 3x +2y = sint, (b)…

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Q: Z is a complex number

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Q: Perform the elementary row operation - R₁ → R₁ to matrix D to obtain matrix E. -1 0 0 01 2 -2 -2 1…

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Q: with y(0) 2 and y/ (0) = -1. y' + 4y = 3 sin 2t

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Q: mperature T of a heated circular plate with the origin being at the ce 64 T(x,y) = x² + y² + 2 point…

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Q: 14- 2x (x-4) (x-1) dx =

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Q: . Find inverse Laplace:

A: Note: As per Bartleby guidelines, we cannot author handwritten answers, so I am giving type written…

Q: Q5. Check whether the given points A (1, 2, 3), B (3, -1, 4) and C (-2, 3, -4) are collinear.

A: If there points A,B,C are co linear then we can have  |AB|+|AC|=|BC| . (A,B,C may have interchanged…

Q: -8s +8 s288 +1 you obtain an equivalent expression given by: s-4 a ~ { ( 2 = ²4 ) ² = 2 ² } + 82 -¹…

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