3. Find general Golution y" + y= Secx

Q: The point on the curve y = 2-x nearest to (3,2) is (1,1) (0,2)

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Q: dy b) Find the equation of a curve if gradient of the curve at point (x, y) is given by- = 2x3 + x…

A: We have to solve the problem

Q: 16. The value of y' for y = x³ + 2x² – 4 at point (-2, –4) is, I. -4 П. 4 III. 6 IV. 8 | II O IV

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Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: 2. F(x, у) %3D — (у i-2x) y2

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: y®y' – 8y9 = ex ,8,

A: On simplification, we get

Q: 1) y" - 36y = 0.

A:

Q: S. dy |1+5

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Q: 2x-2y+1 5) y' = x-y

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Q: В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D3 + 5D² + 3D - 9)y = 64x²e-3x 2. (D³ + 13D - 34)y = 25x2…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Determine d²y of the curve x³y³ = 1. dx² d²y dx² X d²y_2y dx²x2 d²y dx² -x+y Odly - 36xy d²y dx²

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Q: What is the auxiliary equation for y"+by'+c=0, b & c is constant. What are the condition for this DE…

A:

Q: 2b). Let y* + 5x2y² + yx = 624. A) Find y'

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Q: Tom wants to invest $500. He invests in a company that predicts his investment will double in value…

A: Initial investment is $500 and the money gets doubled in 3 years.

Q: Derivatives Show that d(y,v)/dv = (1 – v?/c²)-2 for y, = 1/V1- v² /c².

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Q: Determine óx' Determine óy' determine Tx'y'

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Q: 8. Let a2 + xy³ + 2x = 11. Find y"(x) at the point (1, 2). %3D

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Q: 4. Find dyax and d2 x =V4- t , go t²-2t ye t'-2 get'.

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Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

Q: 5) y = V V+ V? + Væ

A: The function: y=x+x2+x

Q: Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3…

A: Given y5=kx5 To find the orthogonal trajectory

Q: Calculate y". 3 y = V1 + 4x

A: Given:y=1+4x3

Q: The graph of y=x'-3x-24x +32 is concave upward on the interval (1, oo) because: O'=y"=0 Oy' is…

A: The given function is y=x3-3x2-24x+32

Q: b) x²y + xy = 1 x>0 y(1) = 2

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Q: uppose that x + y = 2. What is y" at the point (1, 1)?

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Q: . Find y", given x² – xy + y2 = 3

A: