: Mark all the ODEs in the list for which the function y(t) = cos(t) is a solution. A) y' = sin(t) B) (y)² + y² = 1 C) y' = y² - t D) y" =-y

Q: 12 3. (sin x)y' +y cos r = r sin a,

A:

Q: Find y' at the point (6, 6) where x sin(x? – y²) + 33 = x? – 3.

A:

Q: Find y" for the following function. y = 4 cos x sin x y" = У'-‑

A:

Q: f(æ) sin(x) T Given f 5 and f' 6. Also let g(x) f(x)cos(x) and h(x) Answe the following: T a) g' ()…

A:

Q: If y = -cos(2t), then y(5)= ?

A:

Q: 8. For the function y = e* + sinx: a. Determine y', y",y",y^),y(5), y(6). b. Describe the pattern…

A: We have to find the differentiations of the give function and find y101.

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: Compute Each Derivative: 1) d tan¯¹ (1 + e²x) dx 2) x²cos-¹(3x4) d dx 3) x(sin-¹(x))² dx

A:

Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: Apply variation of parameters to find a particular solution of y ''' - y' = tan x

A: The given differential equation is y''-y' = tan x.We have to solve this using the variation of…

Q: ) Find y as a function of x if x?y" + 2xy' – 42y = 0, y(1) = 5, y'(1) =-3. y =

A:

Q: Find y' and y". y = cos(sin(90)) y' %3D %3D

A: We have to find

Q: let y=[cos(2x-π)]3 Find y' at x=(π/6)

A: Compute the derivative as follows.

Q: use the Chain rule to find derivative: a) y = cot(412 +9) b) y = y = cos (e?) c) d) y = cos(x²) +1…

A: Solve the givens

Q: 1. Find each derivative. a) y = sin- X c) f(x) = ln- sin x COS X b) y = cos(x² - 2x-8)

A:

Q: 1) Determine the derivative o a) f(x) = -4e*² b) y = cos(3*) c) g(x) = -2 sin3 (2x) %3D %3D

A: Note: Multiple subparts are given, we are answered with first three parts only, if you need more…