A molecule is moving along the x-axis such that at any timet 2 0 (in seconds), its position from the origin is given by s(t) = 2t3 – 21t? + 72t – 700 feet.

Q: Find d2y/dx2 in terms of x and y. x2y2-10x=1

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Q: y" - 6y' + qy 2,

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Q: a) Solve y' = 3x² + y, y(0) = 4 by choosing step length 0.1 for y(0.2) by Euler's improved method

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Q: If y2 is negative, then y1 + y2 will lie _______ y1 by a distance equal to ____.

A: If y2  is negative, then y1+y2  will lie _______ y1  by a distance equal to ____.

Q: Between 2005 and 2009, the percentage of people who own a home has changed drastically from state to…

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Q: Solve the non-homo. D.E. 1.y" + y = 3e2x

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Q: Find d2y/dx2 implicitly in terms of x and y.    x2y − 4x = 5

A: To find the second derivative of y implicitly in terms of x and y.

Q: Find the general solution of (T^2 + 4)y' + 2ty = t^2 (t^2 + 4) with the variation of parameters…

A: In this question, we find the general solution of (t2+4)y'+2ty=t2(t2+4) with the variation of…

Q: Y Is the midpolnt of XZ.If XZ 8x-4 and YZ = 3x +1, find x.

A: Given Y is the mid-point of line segment XZ XZ = 8x-4 YZ = 3x+1   to solve the given question use…

Q: Calculate y*)(0) for 0 < k < 5, where y = x* + ax³ + bx² + cx +d (with a, b, c, d the constants).

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Q: Find dy for given Values OF x and AX y= 4x315x X=-3 and AX = 0.3

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Q: Find ax dy x-2–1 given y = 2x3

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Q: , y = X = t+2 t+2,

A: The solution of the problem is given in the next step.

Q: 2s (s² + 1)² 3) Find L¹ 40 by using the convolution theorem.

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Q: Use undetermined coefficients to find the particular solution to y'' - y = 4e t Y(t) =

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Q: 2 Find dyif y.+3x-7 and x =, 2t +1

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: Solve y′ = t − 5ty using both separable and linear methods, and verify that your answers are the…

A: Given data:   The given differential equation is: y’=t-5ty.     The given differential equation can…

Q: 4' for T- T2• T, and T- T1• T2. x - 5y, 4x + 2y) y, 0)

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Q: Find d2y/dx2 implicitly in terms of x and y.    x2 + y2 = 4

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Q: dz Find at (2, -2, 1) if x² + y? + z2 6xz + 6yz + 21

A: Given equation is x2+y2+z2=6xz+6yz+21 We have to find ∂z∂y at 2,-2,1

Q: 9. Solve for y, showing all work: 12x – 4y = 20

A: Using algebraic operation

Q: 6. x = t and y = 3t – 2 for 0Sts4 %3D -

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Q: t² - t dt 0, = (x)6 g'(4) =

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Q: Use the diffecential equation dy= and the initial condition. y=(9)%3T. Fad funchion of 81.

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Q: V Solve usinog variaton of parameters or reduction of order (D²- 2D+1) y = e2"(e*+1)?

A: Solve by using variation of parameter  find auxiliary equation and then find wronskian and put in…

Q: I Sdve for dy using the four-step rule 2. y = x"- x 5X-3 ソ= 4- 3X

A: We have to solve the problem

Q: Is the equation y '(t) = 2y - t separable?

A: Given a differential equation, y't=2y-t

Q: Q3: Find the aven between the curve y,= x+2 and the Carve Y2=-2X+5

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

Q: 1) Suppose you are driving on a straight, level highway without any hills, and your distance away t3…

A: Gas pedal is closest to the floor of the car when the rate of change of distance is 0 or velocity is…

Q: (D* – 4D³ +14D² – 20D +9)y = 0 - -

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Q: Find of z = 2x° 5xy" + x¯ y dy2 -10ху + 3x? у? = -10y + 6xy²

A: To find ∂2z∂y2 of z = 2x3-5xy2+x2y3

Q: Find f(t). 2s + 3 s2 + 4s + 13,

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Q: The y, of y'"-y=2x²-x -3 by using variation of parameters is: .A y,(x)=Ae*+ Be- .B Yp(x) = x – 1 .C…

A: Given that  y"-y=2x^2-x-3 To find the particular solution by using the variation of parameters

Q: (x=1² +3t – 1 + 3t – ; at t=-2. t-2 y = t² +1

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Q: Is the equation t²y' (1) t + 4 - separable? y?

A: t2y't=t+4y2

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

A: Revenue function is given R(x,y) = 19+162x+210y-3x2-5y2-6xy  , it is function of two variable…

Q: Solve the equation using Reduction of Order y" -y = 2et Oy=c₁e¹ + c₂xet + e* (x + c3e-²x + C4)…

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Q: A particle moves on a vertical line so that its coordinate at time t is y=t3 - 12t + 3 , t>0. When…

A: (b)        y = t3 -12t+3    y1 =3t2 - 12 = v(t) when particle moving up means v(t)&gt;0    3t2…

Q: 29. t²y" - 4ty' +6y=0, t>0; y₁(t) = t²

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Q: Q5: 6y²dx-x(2x² + y)dy == 0 (Linear BernoullLeq.)

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Q: Find y' for x°y* + 2x + 2y = 128 at the point (2, – 2). At (2, – 2), y' = Preview -

A: The given equation is: x3y4+2x+2y=128...(1) To find y' at the point (2,-2).

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

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Q: dz Find from the equation x*y+ x z+ z² = 4 ax

A: We differentiate both sides with respect to x, considering z is a function of x.

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find dy ().-0 (27). and X

A: Given 3x2-y2=t2 and y=tsinθ

Q: Solve for y in terms of x and z. z = xy

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: 9. Find a quadratic function y = ao + a1x + a2x² satisfying y(1) = 1, y(-1) = 2, and y'(1) = 2.

A: put values and make equations then solve

Q: Use variation of parameters to obtain the general solution. y''+4y = 4 sec2x

A: The given differential equation is; y"+4y=4sec2x.

Q: Calculate y(k)(0) for 0 ≤ k ≤ 5, where y = x4 + ax3 + bx2 + cx + d (with a, b, c, d the constants).

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Q: Q2 Find2 of y = 4x/x+ vã at x=1? %3D

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Q: Q4. Find the values of the constants a, b, c so that - - F = (axy + bz³)i + (3x² − cz)j + (3xz² –…

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