(a) If b² – 4ac = 0 and y1 = em# solves ay" + by/ + cy = 0, use reduction of order to get a linearly independent solution. [You may assume linear independence]

Q: Solve the particular solution (D2+3D+5)y = 5e-xsin2x using  D- operator method.

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Q: 2y" – 7y" + 12y' + 8y = 0

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Q: Solve the equation using Reduction of Order (D² - 5D + 6) y = 2e* Oy=e+c₁e²x + 2c₂e³x Oy = √² + ₁³x…

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Q: B- Find the fixed point and stability for the difference equation (map) Xn+1 = x + 1.

A: Given difference equation is  xn+1 = x2n + 1…

Q: Find the linearization of f(x) =2x² + 4x – 3 at x= -1

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Q: Find the solution to the 4x + y = 0 4x+y3D -8

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Q: 35. Solve this auxiliary DE y"" – y" – 4y = 0,when x = 4, y = 0

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Q: Solve (x – 2)(x + 1)(x – 4) = 0

A: Question:- solve x-2x+1x-4=0 Here, x-2x+1x-4=0 or we can take it as:- x-2=0 or  x+1=0 or  x+4=0

Q: Solve for the zeros of the quadratic function f(x) = x + 5 – 2x2. 1. Put the quadratic function in…

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Q: 1.у 3D2x? + 3х - 4 - y = Зх- 4 2. у 3 5x?- 7х + 2 3. у %3 3x2-4х +5

A: Topic = Quadratic equations As per guidelines , At a time only three sub-parts of a question can be…

Q: Convert the given quadratic equation to vertex form, i.e., y = a(x – h)² + k. y = x2 + 6x – 9

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Q: A. Convert the following quadratic functions y ax? + bx + c in the form y = a(x - h) + k 1. y = x² +…

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Q: 6. Choose the correct answer. Find the quadratic equation given the points (-4, 0), (2, 0), and…

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Q: 3- Show that the function y = x³ + 3x + 3 satisfy the y= + xy= - 2y = 0

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Q: 6. Show that the quadratic equation ax² + b – a = 0 (a± 0) has two distinct real roots.

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Q: Find the change of variable x = Py that transforms the quadratic form x Ax into y Dy as shown. -…

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