Verify that the function given is a particular solution to the following equation, ar find the particular solution satisfying the initial condition given. dy +² = y°,x>0; y,(x) = -; y(1) = 2 dx x

Q: Find a formula for the curve y = f (2) given that its slope at the point (x, y) is y² (2+ sin x) and…

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Q: Find the derivative of the function. 1 In(1 + 49x 14 y = x arctan 7x dy

A: Given y = xtan-1(7x) -114ln(1+49x2)dydx = d xtan-1(7x) -114ln(1+49x2)dxdydx =…

Q: A3) Find the equation of the line tangent to the graph of f(x) = 4x³ + 3x? – 2x – 8 at x = -2.

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Q: Find the equation of y, given the derivative and the indicated point on the curve. I y = dx = 2(x -…

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Q: Let xy = 2y + x. If you implicitly differentiate this dy equation, and then solve for you dx (a-y)…

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Q: If f(x) = 4x? 6x + 7, find f'(– 2). - Use this to find the equation of the tangent line to the…

A: AnswerGiven f(x)=4x2-6x+7f'(x)=ddx(f(x))wktddx(xn)=nxn-1f'(x)=ddx(4x2-6x+7)f'(x)=8x-6at…

Q: The curve C with equation y = f(x) passes through the point (1, -3). Given the following, find f(x)…

A: We know, ∫xndx= x(n+1)/(n+1)

Q: If y = 2 + cos (x), find the equation of the tangent line to the curve at x = 37. Tangent line:

A: Topic - Equation of tangent line to curve We are given an equation of the curve y=2+cos(x)

Q: Seven thieves try to share a hoard of gold bars equally between themselves. Unfortunately, six bars…

A: Seven thieves try to share a hoard of gold bars equally between themselves.Unfortunately, six bars…

Q: 2. Determine the derivative of g(t) = 8°[(2t + 1)² + t].

A: Given that     g(t) = 8t[(2t+1)2+t]

Q: B. Find the first and second derivatives of the following: 1. m(x) = 2(x)(√x) 2. a(x) = √3x 3. [u(x)…

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Q: Find the equation of the curve that passes through the point (8, 6) if its slope is given by dy = 5x…

A: Given that, the curve passes through the point 8,6 and the slope is given by dydx=5x-7

Q: A particle is moving along the x-axis so that at any time t > 0, its acceleration is given by the…

A: The acceleration of a particle is the rate of changing of velocity at time. When the velocity…

Q: d²y Find the second derivative, dx2 a. x = t² + 1 and y = t³ t2 b. x = 2 · + 2 and y = sin(t + 1)

A: This question can be solved using the concept of second order derivative.

Q: For the function y = 10 e¤ the second order derivative dy is dx? -3 10e + 4x -3 O 10e – 4x 1 10e +…

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Q: Find the equation of y, given the derivative and the indicated point on the curve. y = dy = 2(x - 1)…

A: y= x^2 - 2x + 3

Q: 5x² + 3xy = 3y², find the derivative dy da. as a function of x and y.

A: Consider the equation

Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.