Find particular solutions for the following nonhomogeneous ODEs. (a) y′′ − 3y′ + 2y = (1 + x)e^3x (b) y′′ + 2y′ + y = (2 + 3x)e^−x (c) y′′ + 2y′ + y = (6 cos(x) + 17 sin(x)) e^x.

Q: f" (x) = cos(x), f(0) = -2, f' (0) = -2, f" (0) = 6.

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Q: 1. Find the first and second derivatives. (a) f(x) = e + x³ (b) g (t) = sin(t) + 2 cos (t) (c) h(x)…

A: according to bartleby guide line we do only first part of multiple questions.(a) given

Q: 3. (a) (10) Let g(x) Find g'(x). Don't try to simplify your answer. In(4.x) – cos(2x)

A: Given function g(x) is differentiate w.r.t x as written below:

Q: 6. Find the following derivatives. d (a) a (x²/³ e² (cos (2) - e-*x) sin (2x)) dx (b) tan (30)…

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Q: (a)Deduce the 1$, 20d and 3rd derivatives of y = cos²x.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1 Find the derivative of g(x)= (x)sec(x) + a+ x* + cos - sin(x)

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Q: (a) If (In a] = , evaluate dx d [In x²] dx

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: (a) Let f(x) = (3x – 7) *". Find f2®(x). 49 (b) Let g(x) = cos(9x +2). Find gº" (34) '(x).

A: Consider the part (a): Consider the following function: fx=3x-749…

Q: Find the derivative of (a) (교2 + 1)" (6) In(cos²(e2")) 2x (c) sin-1 e-1 dt x +1 In a

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Q: g (x) = (x + 1) (x – 5)

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Q: f ‴(x) = cos(x),    f(0) = 4,    f ′(0) = 6,    f ″(0) = 7 Find f.

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Q: d 1 (a) / (₁2²+ = + 2²/² +6² +5) X dx d ex (b) (x³ sin(z) +2+1) dx d (ln(tan-¹(x))) dx (c)

A: The given problems can be solved using chain rule of differentiation.

Q: (1) Integrate the following functions: (a) I = [ (4x³ − 6x² + 2x²³¹′)dx (²-3)dx 2 (b) I = .3 (c) I =…

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Q: Integrate e* cos(x) dr COS

A: To evaluate: ∫02πexcosxdx To solve this we will use integration by parts

Q: Find the derivative of y=2ecos.x)(sin(5x)) d'y Calculate as a function of t if x=t-t and y=t-t 2 dx?…

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Q: If f(x) = cos(2x), which of the equations below describes the average rate of change of f(x) over…

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Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

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Q: (d). If (2, 3) are the coordinates of a point on the graph of y = f(x), then the point (2, –4) would…

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Q: Solve y = (1 + y) sec (x) + tan (x) a. y = (x + c) [sec (x) + tan (x)] b. y = (c x) [sec (x) + tan…

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Q: #17 Determine the equations of function graphed below.

A: According to question We have to calculate the equation of the graph.

Q: Consider the following. 1 - 2x² x42x² + 3 Let u(x) = 1 - 2x² and v(x) = x² − 2x² + 3. Find each…

A: We need to find derivative.

Q: (2) Find the derivatives of the following functions. (a) f(0) = cos(0) + 2 tan(0) + sin (7) (b) (c)…

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Q: 1. Find the derivative dy/dr for the function y = f(r) defined implicitly by (x, y)=0 with p(x, y) =…

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